Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777759 | Topology and its Applications | 2017 | 10 Pages |
Abstract
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 Ïk if and only if X is hemicompact. Less demanding but still applicable problem asks whether Ïk has an NN-decreasing base at zero (Uα)αâNN, 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 Ïp and the bounded-open topology Ïb such that (C(X),T) is either metrizable or is an (LM)-space or even has a G-base.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
J.C. Ferrando, S. Gabriyelyan, J. Ka̧kol,