$ KC $-bitopological spaces

Hamza Qoqazeh; Ali Atoom; Maryam Alholi; Eman ALmuhur; Eman Hussein; Anas Owledat; Abeer Al-Nana; Hamza Qoqazeh; Ali Atoom; Maryam Alholi; Eman ALmuhur; Eman Hussein; Anas Owledat; Abeer Al-Nana

doi:10.3934/math.20241545

AIMS Mathematics

2024, Volume 9, Issue 11: 32182-32199. doi: 10.3934/math.20241545

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$ KC $-bitopological spaces

1.
Faculty of Science and Information Technology, Department of Mathematics, Irbid National University, Irbid, Jordan
2.
Faculty of Science, Department of Mathematics, Ajloun National University, Ajloun, Jordan
3.
Faculty of Applied, Taibah University, Al Ula, Saudi Arabia
4.
Faculty of Arts and Science, Department of Mathematics, Applied Science Private University, Amman, Jordan
5.
Faculty of Arts and Science, Department of Mathematics, Amman Arab University, Amman, Jordan
6.
Ministry of Education, Amman, Jordan
7.
Faculty of Science, Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia

Received: 20 August 2024 Revised: 29 October 2024 Accepted: 05 November 2024 Published: 13 November 2024
MSC : 54A05, 54A10, 54A20, 54D25, 54D30

A topological space $ \left(X, \tau \right) $ is called a $ KC $-space when every compact subset of $ X $ is closed. The aim of this paper is to introduce new, namely $ KC $-bitopological spaces and pairwise $ KC $-topological spaces "$ P $-$ KC $-topological spaces". We examined the properties of these concepts and showed the relationships between these concepts and other bitopological spaces. We also discussed the effect of some types of functions on $ KC $-bitopological spaces and pairwise $ KC $-topological spaces. Several examples are discussed, and many well-known theories are generalized.
- bitopological space,
- $ KC $-spaces,
- $ P $-$ KC $-spaces,
- $ K $-function,
- compact function,
- $ P $-Hausdorff,
- $ P $-compact
Citation: Hamza Qoqazeh, Ali Atoom, Maryam Alholi, Eman ALmuhur, Eman Hussein, Anas Owledat, Abeer Al-Nana. $ KC $-bitopological spaces[J]. AIMS Mathematics, 2024, 9(11): 32182-32199. doi: 10.3934/math.20241545

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Abstract

A topological space $ \left(X, \tau \right) $ is called a $ KC $-space when every compact subset of $ X $ is closed. The aim of this paper is to introduce new, namely $ KC $-bitopological spaces and pairwise $ KC $-topological spaces "$ P $-$ KC $-topological spaces". We examined the properties of these concepts and showed the relationships between these concepts and other bitopological spaces. We also discussed the effect of some types of functions on $ KC $-bitopological spaces and pairwise $ KC $-topological spaces. Several examples are discussed, and many well-known theories are generalized.

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