Extension of fragmented Baire-one functions on Lindel\"{o}f spaces
Olena Karlova, Volodymyr Mykhaylyuk
TL;DR
This paper explores conditions under which fragmented Baire-one functions defined on Lindelöf subspaces can be extended to larger completely regular spaces, providing necessary and sufficient criteria.
Contribution
It establishes a comprehensive set of conditions characterizing when fragmented Baire-one functions can be extended from Lindelöf subspaces to any completely regular superspace.
Findings
Identifies necessary and sufficient conditions for extension.
Characterizes extendability of fragmented Baire-one functions.
Provides a framework for extending functions in topological spaces.
Abstract
We investigate the possibility of extension of fragmented functions from Lindel\"{o}f subspaces of completely regular spaces and find necessary and sufficient conditions on a fragmented Baire-one function to be extendable on any completely regular superspace
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Advanced Topology and Set Theory