Topologies on $X$ as points in $2^{\mathcal{P}(X)}$

Jorge L. Bruno; Aisling E. McCluskey

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arXiv · 1111.3212

Topologies on $X$ as points in $2^{\mathcal{P}(X)}$

Jorge L. Bruno·Aisling E. McCluskey

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Abstract

A topology on a nonempty set $X$ specifies a natural subset of $\mathcal{P}(X)$. By identifying $\mathcal{P}(\mathcal{P}(X))$ with the totally disconnected compact Hausdorff space $2^{\mathcal{P}(X)}$, 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 $2^{\mathcal{P}(X)}$ to be compact.

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BibTeX RIS

Jorge L. Bruno, Aisling E. McCluskey. 2011-12-08. Topologies on $X$ as points in $2^{\mathcal{P}(X)}$. https://arxiv.org/abs/1111.3212

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