Monotone retractability and retractional skeletons
arXiv:1403.4480 · doi:10.1016/j.jmaa.2014.09.029
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-Hern{á}ndez 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. Kubiś.
arXiv comment14 pages
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Cited by in corpus (6)
- Projectional skeletons and Markushevich bases
- Families of retractions and families of closed subsets on compact spaces
- On projectional skeletons in Vašák spaces
- Characterization of (semi-)Eberlein compacta using retractional skeletons
- -skeletons on the Alexandroff duplicate
- On the class of continuous images of non-commutative Valdivia compacta