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Open, Connected Functions

Published online by Cambridge University Press:  20 November 2018

Louis Friedler
Louis Friedler*
Affiliation:
University of Alberta, Edmonton Alberta
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Recall that a function f:X→ Yis called connected if f(C) is connected for each connected subset C of X. These functions have been extensively studied. (See Sanderson [6].) A function f:X → Y is monotone if for each y ∊ Y, f-1(y) is connected. We shall use the techniques of multivalued functions to prove that if f: X→ Y is open and monotone onto Y, then f-1(C) is connected for each connected subset C of Y. This result is used to prove that the product of semilocally connected spaces is semilocally connected and that the image of a maximally connected space under an open, connected, monotone function is maximally connected.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 57 - 60
Copyright
Copyright © Canadian Mathematical Society 1973

References

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