English

Separation axioms as lifting properties

General Topology 2017-06-29 v1 Category Theory

Abstract

We observe that many of the separation axioms of topology (including T0T4T_0-T_4) can be expressed concisely and uniformly in terms of category theory as lifting properties (in the sense of Quillen model categories) with respect to (usually open) continuous maps of finite spaces (involving up to 4 points) and the real line.

Keywords

Cite

@article{arxiv.1706.09164,
  title  = {Separation axioms as lifting properties},
  author = {Misha Gavrilovich},
  journal= {arXiv preprint arXiv:1706.09164},
  year   = {2017}
}

Comments

7p

R2 v1 2026-06-22T20:31:53.717Z