Characterizing Corson and Valdivia compact spaces

TL;DR

This paper provides new characterizations of Valdivia and Corson compact spaces using dense subspaces and $c$-skeletons, solving an open problem and introducing new concepts in topology.

Contribution

It introduces a new characterization of Valdivia compact spaces via dense commutatively monotonically retractable subspaces and defines full $c$-skeletons to characterize Corson compact spaces.

Findings

Valdivia spaces characterized by dense commutatively monotonically retractable subspaces

Corson spaces characterized by the existence of a full $c$-skeleton

Solved Problem 5.12 from previous literature

Abstract

We give a new characterization of Valdivia compact spaces: A compact space is Valdivia if and only if it has a dense commutatively monotonically retractable subspace. This result solves Problem 5.12 from \cite{sal-rey}. Besides, we introduce the notion of full $c$-skeleton and prove that a compact space is Corson if and only if it has a full $c$-skeleton.