
TL;DR
This paper introduces $rak P_0$-spaces, a class of regular topological spaces with countable Pytkeev networks, exploring their properties, examples, and stability under various topological operations.
Contribution
It defines $rak P_0$-spaces, studies their properties, and shows their stability under operations like subspaces, products, and function spaces, extending the class of known topological spaces with these features.
Findings
$rak P_0$-spaces include all metrizable separable spaces.
Closed under subspaces, countable products, and certain limits.
Function spaces and free topological groups over $rak P_0$-spaces are also $rak P_0$.
Abstract
A regular topological space is defined to be a -space if it has countable Pytkeev network. A network for is called a Pytkeev network if for any point , neighborhood of and subset accumulating at a there is a set such that and is infinite. The class of -spaces contains all metrizable separable spaces and is (properly) contained in the Michael's class of -spaces. It is closed under many topological operations: taking subspaces, countable Tychonoff products, small countable box-products, countable direct limits, hyperspaces of compact subsets. For an -space and a -space the function space endowed with the compact-open topology is a -space. For any sequential -space the free…
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Philosophy and Theoretical Science
