Metrizable-like locally convex topologies on C(X)

0480760 - MÚ 2018 RIV NL eng J - Článek v odborném periodiku
Ferrando, J.C. - Gabriyelyan, S. - Kąkol, Jerzy
Metrizable-like locally convex topologies on C(X).
Topology and its Applications. Roč. 230, 1 October (2017), s. 105-113. ISSN 0166-8641. E-ISSN 1879-3207
Grant CEP: GA ČR GF16-34860L
Institucionální podpora: RVO:67985840
Klíčová slova: (LM)-topology * functionally bounded set * G-base
Obor OECD: Pure mathematics
Impakt faktor: 0.549, rok: 2017
http://www.sciencedirect.com/science/article/pii/S016686411730370X?via%3Dihub

The classic Arens theorem states that the space C(X) of real-valued continuous functions on a Tychonoff space X is metrizable in the compact-open topology Tk if and only if X is hemicompact. Less demanding but still applicable problem asks whether Tk has an NN-decreasing base at zero (U\alpha)\alpha\inNN, called in the literature a G-base. We characterize those spaces X for which C(X) admits a locally convex topology T between the pointwise topology TP and the bounded-open topology Tb such that (C(X),T) is either metrizable or is an (LM)-space or even has a G-base.
Trvalý link: http://hdl.handle.net/11104/0276458