A general scheme for separably reducible properties
M. Fabian, A. Ioffe, J.P. Revalski
TL;DR
This paper introduces a broad framework for analyzing properties in metric spaces that can be reduced to separable cases, and demonstrates its application to Lipschitz properties and slopes.
Contribution
It presents a novel general scheme for studying separably reducible properties and applies it to establish separable determinacy results for Lipschitz functions and slopes.
Findings
Established separable determinacy of Lipschitz property
Proved separable determinacy of slopes
Provided a unified framework for separably reducible properties
Abstract
We propose a general scheme for studying separably reducible properties in metric spaces and then apply it to obtain separable determinacy of Lipschitz property and the separable determinacy of slopes
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Fixed Point Theorems Analysis