Topological properties of function spaces over ordinal spaces

0477380 - MÚ 2018 RIV ES eng J - Článek v odborném periodiku
Gabriyelyan, S. - Grebík, Jan - Kąkol, Jerzy - Zdomskyy, L.
Topological properties of function spaces over ordinal spaces.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 111, č. 4 (2017), s. 1157-1161. ISSN 1578-7303. E-ISSN 1579-1505
Grant CEP: GA ČR GF16-34860L
Institucionální podpora: RVO:67985840
Klíčová slova: Ascoli * rK-space * ordinal space
Obor OECD: Pure mathematics
Impakt faktor: 1.074, rok: 2017
https://link.springer.com/article/10.1007%2Fs13398-016-0354-7

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(k) and Ck(k) over ordinals k. We prove that Cp(k) is always an Ascoli space, while Cp(k) is a kR-space iff the cofinality of k is countable. In particular, this provides the first Cp-example of an Ascoli space which is not a kR-space, namely Cp(\omega 1). We show that Ck(k) is Ascoli iff cf(k) is countable iff Ck(k) is metrizable.
Trvalý link: http://hdl.handle.net/11104/0273743