Title

Dense Subsets of Function Spaces with No Non-Trivial Convergent Sequences

Author(s)

Vladimir V. Tkachuk, Universidad Autonoma Metropolitana - IztapalapaFollow

Document Type

Plenary Lecture

Publication Date

6-2017

Publication Source

32nd Summer Conference on Topology and Its Applications

Abstract

We will show that a monolithic compact space X is not scattered if and only if C_p(X) has a dense subset without non-trivial convergent sequences. Besides, for any cardinal κ ≥ c, the space R^κ 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 ⊂ C_p(X) has a dense subspace without non-trivial convergent sequences. We also prove that for any countably compact sequential space X, if C_p(X) has a dense k-subspace, then X is scattered.

Comments

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Copyright

Copyright © 2017, the Author

eCommons Citation

Tkachuk, Vladimir V., "Dense Subsets of Function Spaces with No Non-Trivial Convergent Sequences" (2017). Summer Conference on Topology and Its Applications. 50.
https://ecommons.udayton.edu/topology_conf/50