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AUTHOR(S): Nabeela Abu-Alkishik, Eman Almuhur, Hamza Qoqazeh, Ali A. Atoom
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TITLE Results Concerning Paracompact and Strongly Paracompact Spaces |
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ABSTRACT In the present study, we introduce the notion of properly closed hereditary qualities in topological spaces. We discuss whether precompact, metacompact, and 𝑘-spaces display the correctly closed hereditary character. By providing definitive answers to these queries and introducing characterizations of these spaces, a contribution to a deeper comprehension of the topological structures of paracompact and metacompact spaces is offered. Notably, we showed that the space 𝐸 is strongly paracompact if and only if it is paracompact and extending a well-known statement concerning locally compact spaces. In closing, some new findings on paracompact spaces are presented, which contribute to the current discussion in this area and shed light on the complex interrelationships among topological features—using strict proofs and comprehensive. We show that the space 𝐸 is strongly paracompact if and only if it is paracompact, notably extending a well-known result concerning locally compact spaces. Additional discoveries about paracompact spaces are presented after the work, contributing to the current discussion on this topic and providing insightful information on the complex interrelationships among topological aspects. Our work advances the investigation of topological spaces and their inherent qualities by providing robust proof and indepth analysis. |
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KEYWORDS 𝛼 −paracompact space, 𝛼 −Metacompact space, strongly paracompact space |
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Cite this paper Nabeela Abu-Alkishik, Eman Almuhur, Hamza Qoqazeh, Ali A. Atoom. (2024) Results Concerning Paracompact and Strongly Paracompact Spaces. International Journal of Mathematical and Computational Methods, 9, 71-77 |
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