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

Jorge L. Bruno; Aisling E. McCluskey

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

General Topology 2011-12-09 v2

Authors: Jorge L. Bruno , Aisling E. McCluskey

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.

Keywords

general topology topological complexity topological groups

Cite

@article{arxiv.1111.3212,
  title  = {Topologies on $X$ as points in $2^{\mathcal{P}(X)}$},
  author = {Jorge L. Bruno and Aisling E. McCluskey},
  journal= {arXiv preprint arXiv:1111.3212},
  year   = {2011}
}

Comments

First of two papers. 6 pages

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

Abstract

Keywords

Cite

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