Abstract
A Tychonoff space X is called (sequentially) Ascoli if every compact subset (resp. convergent sequence) of Ck(X) is equicontinuous, where Ck(X) denotes the space of all real-valued continuous functions on X endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a pseudocompact space X is Asoli iff it is sequentially Ascoli iff it is selectively ω-bounded. The class of selectively ω-bounded spaces is studied.
Original language | American English |
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Article number | 174 |
Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
Volume | 114 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2020 |
Keywords
- Ascoli
- C(X)
- Compact-covering map
- Pseudocompact
- Selectively ω-bounded
- Sequentially Ascoli
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Computational Mathematics
- Applied Mathematics