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http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/6164
Title: | Ip-Connectedness and Ip-compactness in ideal topological spaces |
Authors: | Rakshana, S. Elango, P. |
Keywords: | Ideals;Ip-Connectedness;Ip-Compactness |
Issue Date: | 2022 |
Publisher: | University of Jaffna |
Abstract: | In ideal topological spaces, we introduce a new class of generalized closed sets known as Ip-closed sets. A subset A of an ideal topological space (X, τ, I) is said to be Ip-closed set if A∗ ⊆ U whenever A ⊆ U and U is preopen. The complement of a Ip-closed set is said to be an Ip-open set. Using these Ipopen sets, we introduced a new class of connectedness and compactness called Ip-connectedness and Ip-compactness in ideal topological spaces. In this context, Ip-connectedness is defined as an ideal topological space (X, τ, I) is said to be Ip-connected if X cannot be written as the disjoint union of two non-empty Ip-open sets. If X is not Ip-connected, it is said to be Ipdisconnected. We concentrated on some of their most important characteristics. The combination of the Ip-irresolute surjective map established one of the features in the Ip-connectedness. They were also related to other types of connectedness, such as Ig-connectedness, Irgconnectedness, and αIg-connectedness, which have definitions similar to Ipconnectedness in ideal topological spaces. Comparatively, we examine compactness: an ideal topological space is said to be Ip-compact if it has a finite subcover for every Ip-open cover of X. We concluded that by similarly investigating the properties of Ip-compactness, which are the same as Ipconnectedness. |
URI: | http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/6164 |
Appears in Collections: | VRC - 2022 |
Files in This Item:
File | Description | Size | Format | |
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Ip-Connectedness and Ip-compactness in ideal topological spaces.pdf | 147.94 kB | Adobe PDF | View/Open |
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