Universally complete spaces of continuous functions
Jan Harm van der Walt
TL;DR
This paper characterizes Tychonoff spaces X for which the space of continuous functions C(X) is universally σ-complete and universally complete, providing a comprehensive understanding of the conditions for these completeness properties.
Contribution
It offers a novel characterization of Tychonoff spaces ensuring C(X) has universal completeness properties, advancing the theory of function spaces.
Findings
C(X) is universally σ-complete for certain Tychonoff spaces
C(X) is universally complete under specific conditions
Provides criteria linking space properties to function space completeness
Abstract
We characterise Tychonoff spaces X so that C(X) is universally {\sigma}-complete and universally complete, respectively.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory