Selections, Paracompactness and Compactness
Mitrofan M. Choban, Ekaterina P. Mihaylova, Stoyan I. Nedev
TL;DR
This paper characterizes the Lindelöf number and degree of compactness of certain topological spaces using selections of lower semi-continuous mappings into complete metrizable or discrete spaces.
Contribution
It introduces new characterizations of Lindelöf number and compactness degree via selection theory for paracompact spaces.
Findings
Lindelöf number characterized through selections
Degree of compactness linked to lower semi-continuous mappings
Results apply to cozero-dimensional kernels of paracompact spaces
Abstract
In the present paper, the Lindelof number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis