Monotone retractability and retractional skeletons

Abstract

We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson.

This gives an answer to a question of R. Rojas-Hernandez and V.V.

Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W.

Kubis.

Keywords

• Retraction
• Monotonically retractable space
• Corson compact space
• Retractional skeleton