Extensions of Continuous Function in LG-Topology

TL;DR

This paper introduces three new maps in LGT-space theory that extend continuous functions and explores related concepts like quotient, decomposition, and isomorphism, enhancing the understanding of LG-topology.

Contribution

It proposes three new maps extending continuous functions in LGT-spaces and studies related natural notions such as quotient, decomposition, and isomorphism.

Findings

OLG, CLG, and LG maps extend continuous functions in LGT-spaces

Introduces and studies quotient, decomposition, weak LG-topology, and isomorphism concepts

Shows these maps have properties similar to continuous functions

Abstract

In this article we introduce three maps, OLG, CLG and LG in LGT-space literature and show that these maps are extension of the continuous function in LGT-spaces and have the almost properties of the continuous functions. Also, it has been introduced and studied the natural notions, quotient, decomposition, weak LG-topology and isomorphism, related to the continuous function.