Very I-favorable spaces
A. Kucharski, Sz. Plewik, V. Valov

TL;DR
This paper characterizes very I-favorable spaces as almost limit spaces of specific inverse systems and links Tychonoff very I-favorable spaces with d-openly generated spaces.
Contribution
It provides a new characterization of very I-favorable spaces using inverse systems and establishes their relation to d-openly generated spaces.
Findings
Very I-favorable spaces are characterized as almost limit spaces of $\sigma$-complete inverse systems.
Tychonoff very I-favorable spaces with respect to co-zero sets are exactly the d-openly generated spaces.
The paper bridges the concepts of inverse systems, d-open maps, and I-favorability in topological spaces.
Abstract
We prove that a Hausdorff space is very -favorable if and only if is the almost limit space of a -complete inverse system consisting of (not necessarily Hausdorff) second countable spaces and surjective d-open bonding maps. It is also shown that the class of Tychonoff very -favorable spaces with respect to the co-zero sets coincides with the d-openly generated spaces.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fuzzy and Soft Set Theory · Advanced Banach Space Theory
