A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (x(n)) statistically quasi-Cauchy if st - lim(n ->infinity) d(x(n+1), x(n)) = ...

Recently, it has been proved that a real-valued function defined on a subset E of A. the set of real numbers, is uniformly continuous on E if and only if it is defined on E and preserves quasi-Cauchy sequences of points ...

Recently, it has been proved that a real-valued function defined on an interval A of R, the set of real numbers, is uniformly continuous on A if and only if it is defined on A and preserves quasi-Cauchy sequences of points ...

A function f on a topological space is sequentially continuous at a point u if, given a sequence (x(n)), lim x(n) = u implies that lim f (x(n)) f (u). This definition was modified by Connor and Grosse-Erdmann for real ...

A sequence (x(n)) of points in a topological group is called Delta-quasi-slowly oscillating if (Delta x(n)) is quasi-slowly oscillating, and is called quasi-slowly oscillating if (Delta x(n)) is slowly oscillating. A ...

A sequence (x(n)) of points in a topological group is slowly oscillating if for any given neighborhood U of 0, there exist delta = delta(U) > 0 and N = N(U) such that x(m)-x(n) epsilon U if n >= N(U) and n <= m <= (1+delta)n. ...

A real function f is continuous if and only if (f(x(n))) is a convergent sequence whenever (x(n)) is convergent and a subset E of R is compact if any sequence x = (x(n)) of points in E has a convergent subsequence whose ...