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In this work we study uniformly locally compact, uniformly locally Lindelöf and uniformly locally countably compact spaces. In particular, by using uniform structures, the paracompactness of any locally Lindelöf topological group and the countable paracompactness of any locally countable compact group are obtained. [ABSTRACT FROM AUTHOR]

Continuity is one of most important concepts in many mathematical disciplines. In some situations general notion of continuity is replaced by sequential continuity. Connor and Grosse-Erdmann replaced lim in the definition of sequential continuity of real functions by a linear functional G on a linear subspace of the vector space of all real sequences. Their definition was extended to topological group X by replacing a linear functional G with an additive function defined on a subgroup of the group of all X-valued sequences. In this paper we introduce neutrosophic G-continuity and investigate its properties in neutrosophic topological spaces. [ABSTRACT FROM AUTHOR]

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 G- continuity, 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. [ABSTRACT FROM AUTHOR]

Scientists have always adopted the concept of sequential continuity as an indispensable subject, not only in Topology but also in some other branches of Mathematics. Connor and Grosse-Erdmann gave this concept for real functions by using an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences instead of lim. Afterwards, this concept were adapted to a topological group X by replacing a linear functional G with an arbitrary additive function defined on a subgroup of the group of all X-valued sequences. Furthermore, alternative theorems in generalized setting were given and varied theorems that had not been achieved for real functions were presented. In this investigation, we offer neutrosophic soft G-continuity and analyze its nature in neutrosophic soft topological spaces. [ABSTRACT FROM AUTHOR]