On totally Lindel\"of spaces
Gabriel Fernandes, Guilherme Pinto, Vin\'icius Rocha
TL;DR
This paper explores properties of totally Lindelof spaces, establishing new characterizations, providing counterexamples, and answering open questions in the field of topology.
Contribution
It proves that every Alster space is totally Lindelof, offers a new characterization of regular Alster spaces, and constructs a non-regular totally Lindelof space that is not Alster.
Findings
Every Alster space is totally Lindelof.
Constructed a non-regular totally Lindelof space that is not Alster.
Proved the existence of a Lindelof P-space that is not Frolik.
Abstract
The results in this paper answer three questions asked by (NOBLE, 2019) and give a partial answer to a question asked by (ALSTER, 1988). We prove that every Alster space is totally Lindelof and this gives a new characterization of regular Alster spaces. We construct a non-regular totally Lindelof space that is not Alster and we prove that there exists a Lindelof P-space that is not Frolik.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Algebra and Logic · Advanced Topology and Set Theory