Functions on $n$-generalized Topological Spaces

Authors

  • Cherry Mae Rivas Balingit Central Mindanao University
  • Julius Benitez Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3502

Keywords:

$\mathscr{G}$-continuous maps, $\mathscr{G}$-open maps, $\mathscr{G}$-closed maps, $\mathscr{G}$-homoemorphisms

Abstract

An $n$-generalized topological ($n$-GT) space is a pair $(X,\mathscr{G})$ of a nonempty set $X$ and a collection $\mathscr{G}$ of $n$ $(n\in\mathbb{N})$ distinct generalized topologies (in the sense of A. Cs\'{a}sz\'{a}r [1]) on the set $X$. In this paper, we look into $\mathscr{G}$-continuous maps, $\mathscr{G}$-open and $\mathscr{G}$-closed maps, as well as $\mathscr{G}$-homoemorphisms in terms of $n$-GT spaces and establish some of their basic properties and relationships. Moreover, these notions are also examined with respect to the component generalized topologies of the underlying spaces by defining and characterizing pairwise versions of the said types of mappings.

Author Biography

  • Cherry Mae Rivas Balingit, Central Mindanao University
    A faculty member of the Department of Mathematics at Central Mindanao University holding the rank of Instructor I, and currently finishing PhD in Mtahematics degree at Mindanao State University - Iligan Institute of Technology.

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Published

2019-10-31

Issue

Vol. 12 No. 4: (October 2019)

Section

Nonlinear Analysis

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How to Cite

Functions on $n$-generalized Topological Spaces. (2019). European Journal of Pure and Applied Mathematics, 12(4), 1553-1566. https://doi.org/10.29020/nybg.ejpam.v12i4.3502