<em>β</em><sub><em>I</em></sub>-Compactness, <em>β</em><sub><em>I</em></sub>*-Hyperconnectedness and <em>β</em><sub><em>I</em></sub>-Separatedness in Ideal Topological Spaces
Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1 O−A∈I and 2 A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to...
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| Autores principales: | , , |
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2022
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| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/79892 |
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| Sumario: | Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1 O−A∈I and 2 A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to be cβI-compact, if every cover Oλ:λ∈Λ of A by β-open sets, Λ has a finite subset Λ0 such that A−∪Oλ:λ∈Λ0∈I. The set A is said to be countably βI-compact if every countable cover of A by βI-open sets has a finite sub-cover. An ideal topological space XτI is said to be βI∗-hyperconnected if X−cl∗A∈I for every non-empty βI-open subset A of X. Two subsets A and B of X is said to be βI-separated if clβIA∩B=∅=A∩clβB. Moreover, A is called a βI-connected set if it can’t be written as a union of two βI-separated subsets. An ideal topological space XτI is called βI-connected space if X is βI-connected. In this article, we give some important properties of βI-open sets, βI-compact spaces, cβI-compact spaces, βI∗-hyperconnected spaces, and βI-connected spaces. |
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| ISBN: | 978-1-80355-093-0 |
| DOI: | 10.5772/intechopen.101524 |