A note on the weak topology of spaces C_k(X) of continuous functions

0542801 - MÚ 2022 RIV ES eng J - Článek v odborném periodiku
Kąkol, Jerzy - Moll-López, S.
A note on the weak topology of spaces C_k(X) of continuous functions.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 115, č. 3 (2021), č. článku 125. ISSN 1578-7303. E-ISSN 1579-1505
Grant CEP: GA ČR(CZ) GF20-22230L
Institucionální podpora: RVO:67985840
Klíčová slova: weak topology * convex space
Obor OECD: Pure mathematics
Impakt faktor: 2.276, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s13398-021-01051-1

It is well known that the property of being a bounded set in the class of topological vector spaces E is not a topological property, where a subset B⊂E is called a bounded set if every neighbourhood of zero U in E absorbs B. The paper deals with the problem which topological properties of bounded sets for the space Ck(X) (of continuous real-valued functions on a Tychonoff space X with the compact-open topology) endowed with the weak topology of Ck(X) can be transferred to bounded sets of Ck(Y) endowed with the weak topology, assuming that the corresponding weak topologies of both Ck(X) and Ck(Y) are homeomorphic.
Trvalý link: http://hdl.handle.net/11104/0320146