- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 72 Issue: 1
- New types of connectedness and intermediate value theorem in ideal topological spaces
New types of connectedness and intermediate value theorem in ideal topological spaces
Authors : Ferit Yalaz, Aynur Keskin Kaymakci
Pages : 259-285
Doi:10.31801/cfsuasmas.1075157
View : 9 | Download : 5
Publication Date : 2023-03-30
Article Type : Research
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