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Product Maps and Countable Paracompactness

Published online by Cambridge University Press:  20 November 2018

Harold W. Martin
Harold W. Martin*
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
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In all that follows, we let S denote the space {0, 1, 1/2, … , 1/n, …} with the relative usual topology and i : S → S denote the identity map on S. In this note, by a map or mapping we always mean a continuous surjection. A map f : X → Y is said to be hereditarily quotient if y ∊ int f(V) whenever V is open in X and f-1(y) ⊂ V. E. Michael has defined a map f : X → Y to be bi-quotient if whenever is a collection of open sets in X which covers f-1(y), there exists finitely many f(V), with V ∊ , which cover some neighbourhood of y.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1187 - 1190
Copyright
Copyright © Canadian Mathematical Society 1972

References

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