I would like to know about the technique to check the cardinality properties for the function space C(X, Y), where X is a tychonoff space and Y a metric space, equipped with uniform or fine topology.
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- 2$\begingroup$ Please can you make explicit: What are cardinal properties of $C(X,Y)$? Why has the topology an influence? $\endgroup$Dieter Kadelka– Dieter Kadelka2021-01-22 09:01:57 +00:00Commented Jan 22, 2021 at 9:01
- $\begingroup$ By Cardinality of C(X, Y) endowed with uniform or fine topology, i mean to study the cardinal invariants such as Character, Density, Weight, Cellularity etc. $\endgroup$Mir Aaliya– Mir Aaliya2021-01-31 06:48:25 +00:00Commented Jan 31, 2021 at 6:48
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1 There is a book called Function Spaces with Uniform, Fine and Graph Topologies by Robert A. McCoy, Subiman Kundu, Varun Jindal. I haven´t read it but it has a chapter called Cardinal Functions and Countability Properties. I would start there.
- $\begingroup$ That book contains the cardinality of a special case C(X), that means when Y= real line R. I want to explore the cardinal invariants of the space C(X, Y). $\endgroup$Mir Aaliya– Mir Aaliya2021-01-31 06:49:39 +00:00Commented Jan 31, 2021 at 6:49