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 …

An ideal I is a family of subsets of positive integers N which is closed under taking finite
unions and subsets of its elements. A sequence (xn) of real numbers is said to be I …

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 (xn) statistically quasi-Cauchy if st− lim …

We investigate the impact of changing the definition of convergence of sequences on the
structure of the set of connected subsets of a topological group, X. A non-empty subset A of …

Abstract A sequence (α _ k)(α k) of points in RR, the set of real numbers, is called ρ ρ-
statistically convergent to an element ℓ ℓ of RR if _ n → ∞ 1 ρ _ n|{k ≤ n:| α _ k-ℓ| ≥ ε\}|= 0 …

A function f is continuous if and only if f preserves convergent sequences; that is,(f (αn)) is a
convergent sequence whenever (αn) is convergent. The concept of Nθ‐ward continuity is …

Continuity, in particular sequential continuity, is an important subject of investigation not only
in topology but also in some other branches of mathematics. Connor and Grosse‐Erdmann …

In this paper, the concept of a lacunary statistically-quasi-Cauchysequence is investigated.
In this investigation, we proved interesting theoremsrelated to lacunary …

G-methods and G-continuity for real functions are induced by changing the definition of the
convergence of sequences on the set of real numbers. In this paper we introduce the …

A sequence (xn) of points in a topological group is slowly oscillating if for any given
neighborhood U of 0, there exist δ= δ (U)> 0 and N= N (U) such that xm− xn∈ U if n≥ N (U) …