New types of connectedness and intermediate value theorem in ideal topological spaces

Year 2023, Volume: 72 Issue: 1, 259 - 285, 30.03.2023

Ferit Yalaz , Aynur Keskin Kaymakcı

https://doi.org/10.31801/cfsuasmas.1075157

Abstract

The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce new types of connectedness. It is shown that these new types of connectedness are more general than some previously defined concepts of connectedness in ideal topological spaces. The new types of connectedness are compared with well-known connectedness in point-set topology. Then, the intermediate value theorem for ideal topological spaces is given. Also, for some special cases, it is shown that the intermediate value theorem in ideal topological spaces and the intermediate value theorem in topological spaces coincide.

Keywords

Ideal topological space, local function, local closure function, connected space, separated subset

Thanks

The first author would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for their financial supports during his doctorate studies.

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