Yazar "Mucuk, Osman" seçeneğine göre listele

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    Abstract book
    (Maltepe Üniversitesi, 2019) Çakallı, Hüseyin; Savaş, Ekrem; Sakallı, İzzet; Horgan, Jane; Daly, Charlie; Power, James; Kocinac, Ljubi^sa; Cavalanti, M. Marcelo; Corrˆea, Wellington J.; Özsarı, Türker; Sep´ulveda, Mauricio; Asem, Rodrigo V´ejar; Harte, Robin; Açıkgöz, Ahu; Esenbel, Ferhat; Jabor, Ali Ameer; Omran, Ahmed abd-Ali; Varol, Banu Pazar; Kanetov, Bekbolot; Baidzhuranova, Anara; Saktanov, Ulukbek; Kanetova, Dinara; Zhanakunova, Meerim; Liu, Chuan; Yıldırım, Esra Dalan; Şahin, Hakan; Altun, Ishak; Türkoğlu, Duran; Akız, Hürmet Fulya; Mucuk, Osman; Motallebi, Mohammad Reza; Demir, Serap; Şahan, Tunçar; Kelaiaia, Smail; Yaying, Taja; Noiri, Takashi; Vergili, Tane; Çetkin, Vildan; Misajleski, Zoran; Shekutkovski, Nikita; Durmishi, Emin; Berkane, Ali; Belhout, Mohamed; Es-Salih, Aries Mohammed; Sönmez, Ayşe; Messirdi, Bachir; Derhab, Mohammed; Khedim, Tewfik; Karim, Belhadj; Affane, Doria; Yarou, Mustapha Fateh; Yılmaz, Fatih; Sertbaş, Meltem; Bouchelaghem, Faycal; Ardjouni, Abdelouaheb; Djoudi, Ahcene; Çiçek, Gülseren; Mahmudov, Elimhan; El-Metwally, Hamdy A.; AL-kaff, M.; Mustafayev, Heybetkulu; Duru, Hülya; Biroud, Kheireddine
    On behalf of the Organizing Committee, we are very pleased to welcome you to the 3nd International Confer- ence of Mathematical Sciences (ICMS 2019) to be held between 4-8 September 2019 at Maltepe University in Istanbul. We hope that, ICMS 2019 will be one of the most beneficial scientific events, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in any field of science.
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    Crossed module aspects of monodromy groupoids for internal groupoids
    (Maltepe Üniversitesi, 2019) Mucuk, Osman; Demir, Serap; Şahan, Tunçar
    The notion of monodromy groupoid was introduced by J. Pradines in [3] to generalize the standard construction of a simply connected Lie group from a Lie algebra to a construction of a Lie groupoid from a Lie algebroid and has been developed by many others. The categorical equivalence between internal groupoids and crossed modules in groups with operations is known by [2] as a generalization of an equivalence of crossed modules within groups and group-groupoids [1]. In this work using the former equivalence and techniques of crossed modules we give a construction of the monodromy groupoid for topological internal groupoids within groups with operations including groups, rings, associative algebras, associative commutative algebras, Lie algebras, Leibniz algebras, alternative algebras and some others.
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    G-compactness and local G-compactness of topological groups with operations
    (Maltepe Üniversitesi, 2021) Mucuk, Osman
    It is well known that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of Gcontinuity, G-compactness and G-connectedness. In this paper we prove some results about G-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.
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    G-Connectedness in Topological Groups with Operations
    (UNIV NIS, FAC SCI MATH, 2018) Mucuk, Osman; Cakalli, Huseyin
    It is a well known fact that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of G-continuity, G-compactness and G-connectedness. In this paper we present some results about G-hulls, G-connectedness and G-fundamental systems of G-open neighbourhoods for a wide class of topological algebraic structures called groups with operations, which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.
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    G-sequentially connectedness for topological groups with operations
    (AMER INST PHYSICS, 2016) Mucuk, Osman; Cakalli, Huseyin; Ashyralyev, A; Lukashov, A
    It is a well-known fact that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by l i m from the set of all convergent sequences in X to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing l i m with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of G-sequential continuity, G-sequential compactness and G-sequential connectedness. In this work, we present some results about G-sequentially closures, G-sequentially connectedness and fundamental system of G-sequentially open neighbourhoods for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others.
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    Group-groupoids and crossed module aspects of monodromy groupoids
    (Maltepe Üniversitesi, 2019) Mucuk, Osman; Demir, Serap; Şahan, Tuncar
    In this extended abstract considering the topological version of categorical equivalence of crossed modules and group-groupoids we develop crossed module aspects of monodromy group-groupoids for topological group-groupoids and give some examples for monodromy groupoids.
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    Internal categories in the category of semi abelian algebras
    (Maltepe Üniversitesi, 2021) Mucuk, Osman; Demir, Serap
    In this extended abstract for given an algebraic theory T whose category of models is semi-abelian, we define the internal groupoid in the semi-abelian category of models, and give some results about these internal categories.
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    Internal groupoid actions and liftings of crossed modules within groups with operations
    (AIP Publishing, 2019) Akız, H. Fulya; Mucuk, Osman; Şahan, Tuncar
    In this extended abstract we define the notion of lifting of a crossed module in groups with operations and state some properties of this type of liftings. Furthermore for a certain crossed module we give a categorical equivalence between the lifting of crossed modules and internal groupoid actions in groups with operations.
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    Internal groupoid actions and liftings of crossed modules within groups with operations
    (AIP Publishing, 2019) Akız, H. Fulya; Mucuk, Osman; Şahan, Tunçar
    In this extended abstract we define the notion of lifting of a crossed module in groups with operations and state some properties of this type of liftings. Furthermore for a certain crossed module we give a categorical equivalence between the lifting of crossed modules and internal groupoid actions in groups with operations.
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    Internal groupoid actions and liftings of crossed modules within groups with operations
    (Maltepe Üniversitesi, 2019) Akız, H. Fulya; Mucuk, Osman; Şahan, Tunçar
    In this extended abstract we define the notion of lifting of a crossed module in groups with operations and state some properties of this type of liftings. Furthermore for a certain crossed module we give a categorical equivalence between the lifting of crossed modules and internal groupoid actions in groups with operations.
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    LACUNARY STATISTICALLY UPWARD AND DOWNWARD HALF QUASI-CAUCHY SEQUENCES
    (UNIV PRISHTINES, 2016) Cakalli, Huseyin; Mucuk, Osman
    A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (x(k)) of points in R is called lacunary statistically upward half quasi Cauchy if lim(r infinity) 1/h(r) vertical bar{k is an element of I-r : x(k) - x(k+1) >= epsilon}vertical bar - 0 for every epsilon > 0; and (x(k)) is called lacunary statistically downward half quasi-Cauchy if lim(r ->infinity) 1/h(r) vertical bar {k is an element of I-r : x(k+1) - x(k) >= epsilon}vertical bar = 0 for every epsilon > 0, where theta = (k(r)) is an increasing sequence of non-negative integers such that k(0) = 1 and h(r) : k(r) - k(r-1) -> infinity. We investigate lacunary statistically upward continuity and lacunary statistically downward continuity and prove some interesting theorems. It turns out that not only a lacunary statistically upward continuous function on a below bounded subset, but also a lacunary statistically downward continuous function on an above bounded subset is uniformly continuous.
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    Lacunary statistically upward half quasi-cauchy sequences
    (American Institute of Physics Inc., 2015) Çakallı, Hüseyin; Mucuk, Osman
    A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (xn) of points in R is called lacunary statistically upward half quasi-Cauchy if [EQUATION PRESENTED] for every ? > 0, and ? = (kr) is an increasing sequence ? = (kr) of non-negative integers such that k0 = 1 and hr: kr-kr-1 › . We investigate lacunary statistically upward continuity, and prove interesting theorems. It turns out that any lacunary statistically upward continuous function on a below bounded subset of R is uniformly continuous. © 2015 AIP Publishing LLC.
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    Local group-groupoids
    (Maltepe Üniversitesi, 2009) Mucuk, Osman; Bağrıyanık, Berrin; Ay, Yeşim H.
    The theory of covering groupoids plays an important role in the applications of groupoids (cf. [1], [5]). There are two important results about group-groupoids given in [2]. One is that if X is a topological group whose underlying space has a universal cover, then the category T GCov/X of topological group covers of X is equivalent to the category GpGpdCov/?1X of group-groupoid covers of ?1X. The other is that if G is a group-groupoid, then the category the category GpGdCov/G of covering morphisms over G is equivalent to the category GpGdAct(G) of group-groupoid actions of G on groups is equivalent to equivalent. In this paper we introduce the notion of a local group-groupoid as a local group object in the category of gorupoids and prove local group-groupoid version of these results. For the first result we prove that if L is a local topological group, whose underlying topology has a universal cover, then the category LT GCov/L of local topological covers of L and the category LGGdCov/?1(L) of local group-groupoid covers of ?1(L) are equivalent. For the second result we prove that if G is a local group-groupoid, then the category LGpGdCov/G of local groupgroupoid covers is equivalent to the category LGpGdAct(G) of local group-groupoid actions of G on local groups.
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    Local group-groupoids and local crossed modules
    (Maltepe Üniversitesi, 2021) Akiz, H. Fulya; Mucuk, Osman
    In this paper we define the notion of local crossed module for local groups and prove that these are categorically equivalent to local group-groupoids.
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    Normality and quotient of crossed modules within group with operations
    (Maltepe Üniversitesi, 2019) Şahan, Tunçar; Mucuk, Osman
    In this note we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and give same results on these crossed modules.
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    ON CONNECTEDNESS VIA A SEQUENTIAL METHOD
    (UNION MATEMATICA ARGENTINA, 2013) Cakalli, Huseyin; Mucuk, Osman
    Recently, the first author has introduced a concept of G-sequential connectedness in the sense that a non-empty subset A of a Hausdorff topological group X is G-sequentially connected if the only subsets of A which are both G-sequentially open and G-sequentially closed are A and the empty set empty set. In this paper we investigate further properties of G-sequential connectedness and obtain some interesting results.
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    On G-Compactness of Topological Groups with Operations
    (Univ Nis, Fac Sci Math, 2022) Mucuk, Osman; Cakalli, Hüseyin
    One can notice that if X is a Hausdorff space, then limits of convergent sequences in X give us a function denoted by lim from the set of all convergent sequences in X to X. This notion has been extended by Connor and Grosse-Erdmann to an arbitrary linear functional G defined on a subspace of the vector space of real numbers. Following this idea some authors have defined concepts of G-continuity, G-compactness and G-connectedness in topological groups. In this paper we present some results about G-compactness of topological group with operations such as topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras and many others.
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    Quotients of monodromy groupoids
    (Maltepe Üniversitesi, 2019) Mucuk, Osman; Şahan, Tunçar
    The main object of this extended abstract is to define the quotient groupoid of the monodromy groupoid for a topological group-groupoid using the categorical assignment between crossed modules and group-groupoids and state some results without in detail. The idea of monoromy principle is that a local morphism f on a topological structure G is extended not only to G itself but also to some simply connected cover of G [12, Theorem 2, Chapter 2]. A version of this result was developed in [13] for Lie groups. The notion of monodromy groupoid was introduced by J. Pradines in a series of the works [27, 28, 29, 30] to generalize a standard construction of a simply connected Lie group from a Lie algebra to a corresponding construction of a Lie groupoid from a Lie algebroid (see also [16, 17, 18, 19, 25, 33]). For more discussions about holonomy and monodromy groupoids we refer the readers to [7] and [8]. Let G be a topological groupoid. The monodromy groupoid denoted by Mon(G) is defined by Mackenzie in [17, p.67-70] as a disjoint union of the universal covers of the stars Gx’s. The topological aspect of the monodromy groupoid was developed in [20] using the holonomy technics of [1] and written in Lie groupoid case including topological groupoids in [9] and [10].
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    Topological aspect of monodromy groupoid for a topological internal groupoid
    (Maltepe Üniversitesi, 2019) Akız, Hürmet Fulya; Mucuk, Osman
    The notion of monodromy groupoid was originally introduced by J. Pradines in [4] and has been developed by many others (e.g. [1, 2, 3]). On the one hand, the monodromy groupoid of a topological internal groupoid in groups with operations including groups, rings, associative algebras, associative commutative algebras, Lie algebras, Leibniz algebras, alternative algebras and others is considered in [2]. On the other hand, Mucuk and Demir in [3] developed topological aspect of monodromy groupoid and proved that the monodromy groupoid of a topological groupgroupoid is also a topological group-groupoid. The aim of this paper is to extend the results of latter paper to the former case.