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k-Discreteness and k-Analytic Sets

Published online by Cambridge University Press:  20 November 2018

Ronald C. Freiwald
Ronald C. Freiwald*
Affiliation:
Washington University, St. Louis, Missouri
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All spaces considered here are metrizable. k will always denote an infinite cardinal. The successor of k will be denoted by k+.

Of particular interest will be the Baire spaces where each Tn is a discrete space of cardinal k. The product topology on B(k) is the same as the topology given by the (complete) “first-difference” metric, p : p(s, t) = 1/n if Si = ti for 1 ≦ i ≦ n —1 and sn = tn. A great deal of information about these spaces can be found in [4].

A subset A of X is called k-analytic (in X) if there exist, for each t ∈ B(k), closed subsets F(t1), …, F(t1, …, tn), … of X such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 2 , February 1980 , pp. 331 - 341
Copyright
Copyright © Canadian Mathematical Society 1980

References

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