Functions on $n$-generalized Topological Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i4.3502Keywords:
$\mathscr{G}$-continuous maps, $\mathscr{G}$-open maps, $\mathscr{G}$-closed maps, $\mathscr{G}$-homoemorphismsAbstract
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.Downloads
Published
2019-10-31
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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