The Compact-Open Topology on C(X)
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Beschreibung
This monograph offers a comprehensive study on the classical Compact-Open topology on the space C(X) of all real valued continuous functions on a Tychonoff space X. It makes C(X) a locally convex space. The space C(X) equipped with the compact-open topology k is denoted by C_k(X). In this monograph, the authors have adopted an analytical approach, by considering C_k(X) as a locally convex space. Consequently, the authors give easy and shorter proofs of several results about C_k(X). The authors also provide a short historic perspective on compact-open topology.
This monograph touches almost all aspects of the compact-open topology. In particular, it includes a detailed study of the topological properties of compact-open topology on C(X). A complete chapter is devoted to study compact and dense subsets of the space C_k(X). Since C_k(X) is a locally convex space, in Chapter 8, the authors provide a detailed study of the dual of this locally convex space. In the final chapter, the authors present several functional analytic properties of this locally convex space.
This monograph has a wide appeal to mathematicians in various fields. Chapters 2, 4 and 5 are of interest to topologists, while Chapters 8 and 9 are of interest to functional analysts. Chapters 3, 6 and 7, meanwhile, are of interest to both topologists and functional analysts.
This monograph offers a comprehensive study on the classical Compact-Open topology on the space C(X) of all real valued continuous functions on a Tychonoff space X. It makes C(X) a locally convex space. The space C(X) equipped with the compact-open topology k is denoted by C_k(X). In this monograph, the authors have adopted an analytical approach, by considering C_k(X) as a locally convex space. Consequently, the authors give easy and shorter proofs of several results about C_k(X). The authors also provide a short historic perspective on compact-open topology.
This monograph touches almost all aspects of the compact-open topology. In particular, it includes a detailed study of the topological properties of compact-open topology on C(X). A complete chapter is devoted to study compact and dense subsets of the space C_k(X). Since C_k(X) is a locally convex space, in Chapter 8, the authors provide a detailed study of the dual of this locally convex space. In the final chapter, the authors present several functional analytic properties of this locally convex space.
This monograph has a wide appeal to mathematicians in various fields. Chapters 2, 4 and 5 are of interest to topologists, while Chapters 8 and 9 are of interest to functional analysts. Chapters 3, 6 and 7, meanwhile, are of interest to both topologists and functional analysts.
First dedicated monograph on compact-open topology Covers both topological and functional analytic aspects of the compact-open topology on C(X) Contains more than 300 references related to compact-open topology
Autor*in
Subiman Kundu
Themen in »The Compact-Open Topology on C(X)«
uniform convergence compact-open topology metrizability completeness properties countability properties cardinal invariants evaluation map equicontinuous family compact subsets Ascoli-type theorems dual space Borel measure barreled space bornological Warner bounded