32nd Summer Conference on Topology and Its Applications
We will show that a monolithic compact space X is not scattered if and only if Cp(X) has a dense subset without non-trivial convergent sequences. Besides, for any cardinal κ ≥ c, the space Rκ has a dense subspace without non-trivial convergent sequences. If X is an uncountable σ-compact space of countable weight, then any dense set Y ⊂ Cp(X) has a dense subspace without non-trivial convergent sequences. We also prove that for any countably compact sequential space X, if Cp(X) has a dense k-subspace, then X is scattered.
Copyright © 2017, the Author
Tkachuk, Vladimir V., "Dense Subsets of Function Spaces with No Non-Trivial Convergent Sequences" (2017). Summer Conference on Topology and Its Applications. 50.