A characterization of the compact spaces with a retractional skeleton - Garc´ıa-Ferreira, S.; Yescas-Aparicio, C. (Topology Proceedings, 2022)
In [14] the authors introduced the concept of retractional skeleton ( $r$-skeleton) and they characterized the Valdivia compact spaces with this notion. In [2], the authors introduced the notion of (full) $c$-skeleton which is a pair consisting of a family of closed subsets and an $ω$-monotone map which satisfy certain properties; and they proved that a compact space is a Corson compact space iff it admits a full $c$-skeleton. The main purpose of this article is to prove that a compact space admits a retractional skeleton iff it admits a $c$-skeleton. Moreover, we establish a condition on a $c$-skeleton which allows a compact space be a Valdivia compact space. Additionally, we provide an answer to Question 5.8 of the paper [2] by using an argument different from the one used in [11] to respond to the same question.