Abstract
A topological space X is said to be an Ascoli space if any compact subset K of Ck(Y) is evenly continuous. This definition is motivated by the classical Ascoli theorem. We study the kR-property and the Ascoli property of Cp(κ) and Ck(κ) over ordinals κ. We prove that Cp(κ) is always an Ascoli space, while Cp(κ) is a kR-space iff the cofinality of κ is countable. In particular, this provides the first Cp-example of an Ascoli space which is not a kR-space, namely Cp(ω1). We show that Ck(κ) is Ascoli iff cf (κ) is countable iff Ck(κ) is metrizable.
Original language | English |
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Pages (from-to) | 1157-1161 |
Number of pages | 5 |
Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
Volume | 111 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2017 |
Keywords
- Ascoli
- C(X)
- C(X)
- Ordinal space
- k-space
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Computational Mathematics
- Applied Mathematics