Metrizable-like locally convex topologies on C(X)
| Autor: | Saak Gabriyelyan, Jerzy Ka̧kol, Juan Carlos Ferrando |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pointwise
Discrete mathematics Tychonoff space 010102 general mathematics Zero (complex analysis) Mathematics::General Topology Base (topology) Space (mathematics) 01 natural sciences 010101 applied mathematics Banach–Alaoglu theorem Metrization theorem Geometry and Topology 0101 mathematics Mathematics Strong operator topology |
| Zdroj: | Topology and its Applications. 230:105-113 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2017.07.016 |
| Popis: | 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 τ k if and only if X is hemicompact. Less demanding but still applicable problem asks whether τ k has an N N -decreasing base at zero ( U α ) α ∈ N N , 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 τ p and the bounded-open topology τ b such that ( C ( X ) , T ) is either metrizable or is an ( L M ) -space or even has a G -base. |
| Databáze: | OpenAIRE |
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