About uniformly Lindelöf spaces
Authors: Bekbolot E. Kanetov, Ulukbek A. Saktanov, Meerim O. Zhanakunova
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2021 · Pages: 29 - 34
Published Online: 22 Nov 2021
Abstract: The idea of Lindelöfness is one of the most important in General Topology. There have been some variants in defining uniformly Lindelöfness of uniform spaces. For example, uniform A-Lindelöfness in the sense of L.V. Aparina [1], uniform B-Lindelöfness in the sense of A.A. Borubaev [2], uniform I-Lindelöfness in the sense of D.R. Isbell [5]. In this paper we propose a new approach to the definition of a uniform analogue of Lindelöfness. We introduce and study uniformly Lindelöf spaces.
Keywords: Finitely-additive open covering, locally finite uniform covering, ℵ0-boundedness, uniformly perfect mappings