Ince, Dagci, F.Misirlioglu, T.Akalli, H.Ç.Ko?inac, L.D.R.2024-07-122024-07-1220239.78074E+120094-243X10.1063/5.01758422-s2.0-85177639233https://doi.org/10.1063/5.0175842https://hdl.handle.net/20.500.12415/74726th International Conference of Mathematical Sciences, ICMS 2022 -- 20 July 2022 through 24 July 2022 -- -- 193514If the classical metric axioms on a set X are changed by disregarding the case that d(x, y)=0 implies x=y, the general properties for metric spaces will easily be extended. In this case d is called a pseudo-metric. Neverthless, if the necessity of the symmetry of d is disregarded, the proper extensions of metric consequences are not evident at all. A pseudo-asymmetric on a non-empty set X is a non-negative real-valued function p on X×X such that for x, y, z?X we have p(x, x)=0 and p(x, y)?p(x, z)+p(z, y). If p satisfies the additional condition that p(x, y)=0 implies x=y, then p is an asymmetric metric on X. A set with an asymmetric metric is called an asymmetric space. Since symmetry necessity is not satisfied, there are two kinds of open balls, namely forward balls and backward balls. As a result, there are two kinds of topological notions. Here we give some theorems related to convergence of sequences of functions and forward and backward total boundedness on asymmetric spaces. © 2023 AIP Publishing LLC.eninfo:eu-repo/semantics/closedAccessAsymmetricBackward Convergence.Forward ConvergenceConference Object1N/A2879