Nearness Posets
General Topology
2019-02-22 v1 Category Theory
Abstract
We extend nearness frames to posets representing bases and even subbases of spaces. This allows us to put a classic duality due to Wallman, between compact spaces and abstract simplicial complexes, into a general nearness framework. Within this framework we extend Wallman's duality to locally compact spaces and, with further modifications, to completely metrisable spaces. Moreover, we provide an elementary sublocale-free version of an admissibility condition due to Picado and Pultr and show how it strengthens Wallman's admissibility condition.
Cite
@article{arxiv.1902.07948,
title = {Nearness Posets},
author = {Tristan Bice},
journal= {arXiv preprint arXiv:1902.07948},
year = {2019}
}