Two transfinite chains of separation conditions between T1 and T2

@article{Sequeira2004TwoTC,
  title={Two transfinite chains of separation conditions between T1 and T2},
  author={Luis Sequeira},
  journal={Applied general topology},
  year={2004},
  volume={5},
  pages={265-273}
}
  • L. Sequeira
  • Published 1 October 2004
  • Mathematics
  • Applied general topology
Two new families of separation conditions have arisen in the study of the impact that the algebraic properties of topological algebras have on the topologies that may occur on their underlying spaces. We describe the relative strengths of these families of separation conditions for general spaces. 

An ordinal indexed hierarchy of separation properties

We refine and stratify the standard separation properties to produce a descending hierarchy between T3 and T1. The interpolated properties are related to the patch properties and the Vietoris

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One of the basic results from the theory of topological groups is that aT0 topological group is already completely regular. It is also known [1] thatT0 quasigroups are regular. Taylor [8] showed that

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Abstract. Let P be a property of topological spaces. Let [P] be the class of all varieties $ \scr V $ having the property that any topological algebra in $ \scr V $ has underlying space satisfying