0
$\begingroup$

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.

Improve this question
$\endgroup$
2
  • 2
    $\begingroup$ Please can you make explicit: What are cardinal properties of $C(X,Y)$? Why has the topology an influence? $\endgroup$
    – Dieter Kadelka
    Commented 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
    Commented Jan 31, 2021 at 6:48

1 Answer 1

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$
1
  • $\begingroup$ 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
    Commented Jan 31, 2021 at 6:49

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .