Topologies on X as points in 2^P(X)

2011/11/14 by Jorge Bruno, Jorge L. Bruno, Bruno, Jorge L. +3
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #math.GN

paper · pdf · doi:10.48550/arxiv.1111.3212

First of two papers. 6 pages

openalex publication_date 2011/11/14 · arxiv created 2011/12/08 · arxiv updated 2011/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A topology on a nonempty set X specifies a natural subset of P(X). By identifying P(P(X)) with the totally disconnected compact Hausdorff space 2^P(X), the lattice Top(X) of all topologies on X is a natural subspace therein. We investigate topological properties of Top(X) and give sufficient model-theoretic conditions for a general subspace of 2^P(X) to be compact.

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