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arXiv · 1902.07948

Nearness Posets

Tristan Bice
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Abstract

We extend nearness frames to posets representing bases and even subbases of $T_1$ spaces. This allows us to put a classic duality due to Wallman, between compact $T_1$ spaces and abstract simplicial complexes, into a general nearness framework. Within this framework we extend Wallman's duality to locally compact $T_1$ 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.

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Tristan Bice. 2019-02-21. Nearness Posets. https://arxiv.org/abs/1902.07948

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