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On topological quotient maps preserved by pullbacks or products

Published online by Cambridge University Press:  24 October 2008

B. J. Day  and
G. M. Kelly
B. J. Day
Affiliation:
University of New South Wales, Australia
G. M. Kelly
Affiliation:
University of New South Wales, Australia
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Extract

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:

Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?

Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)

Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 553 - 558
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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