1. Topologies on the space of continuous functions
- Author
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L'ubica Holá, R. A. McCoy, G. Di Maio, and D. Holý
- Subjects
Discrete mathematics ,Weak topology ,Countably compact ,Mathematics::General Topology ,Extension topology ,Fine topology ,Initial topology ,Lower limit topology ,Equinormal ,Proximal graph topology ,Topology of uniform convergence ,Comparison of topologies ,Combinatorics ,Pseudocompact ,Graph topology ,Product topology ,General topology ,Krikorian topology ,Open-cover topology ,Geometry and Topology ,Particular point topology ,Countably paracompact ,Mathematics - Abstract
Let X and Y be Tychonoff spaces and C(X, Y) be the space of all continuous functions from X to Y. The coincidence of the fine topology with other function space topologies on C(X, Y) is discussed. Also cardinal invariants of the fine topology on C(X, R ) , where R is the space of reals, are studied. To answer some questions of Di Maio and Naimpally (1992) other function space topologies are investigated, namely, Krikorian topology, open-cover topology, graph topology, topology of uniform convergence, proximal graph topology.
- Published
- 1998
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