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

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

2011-11-14

arxiv.org/abs/1111.3212v2

Mathematics

General Topology

First of two papers. 6 pages

Scientific paper

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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