Pseudocomplementation in rings of continuous functions
Guram Bezhanishvili, Marcus Tressl
TL;DR
This paper investigates the structure of rings of real-valued continuous functions through pseudocomplementation properties on associated lattices, providing complete characterizations of pseudocomplementation and near-complete for relative pseudocomplementation.
Contribution
It offers a comprehensive analysis of pseudocomplementation in rings of continuous functions and characterizes these properties across different lattice structures.
Findings
Complete characterization of pseudocomplementation in all cases
Almost complete characterization of relative pseudocomplementation
Lattice-based approach to understanding rings of continuous functions
Abstract
We study rings of real-valued continuous functions in terms of pseudocomplementation conditions on various lattices attached to their prime spectrum. We fully characterize pseudocomplementation in all cases and have an almost complete characterization of relative pseudocomplementation.
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