THEORY OF GENERALIZED CONNECTEDNESS (g-Tg-CONNECTEDNESS) IN GENERALIZED TOPOLOGICAL SPACES (Tg-SPACES)

Authors : Mohammad Irshad KHODABOCUS, Noorulhacq SOOKIA

Pages : 1-38

Doi:10.33773/jum.1149387

View : 37 | Download : 14

Publication Date : 2023-01-31

Article Type : Research Paper

Abstract :In this paper, the definitions of novel classes of generalized connected sets insert ignore into journalissuearticles values(briefly, g-Tg-connected sets); and generalized disconnected sets insert ignore into journalissuearticles values(briefly, g-Tg-disconnected sets); in generalized topological spaces insert ignore into journalissuearticles values(briefly, Tg-spaces); are defined in terms of generalized sets insert ignore into journalissuearticles values(briefly, g-Tg -sets); and, their properties and characterizations with respect to set-theoretic relations are presented. The basic properties and characterizations of the notions of local, pathwise, local pathwise and simple g-Tg-connectedness are also presented. The study shows that local pathwise g-Tg -connectedness implies local g-Tg-connectedness, pathwise g-Tg-connectedness implies g-Tg-connectedness, and g-Tg-connectedness is a Tg-property. Diagrams establish the various relationships amongst these types of g-Tg-connectedness presented here and in the literature, and a nice application supports the overall theory.
Keywords : Generalized topological space Tg spaces, generalized local connectedness local g Tg connectedness, generalized pathwise connectedness insert ignore into journa

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