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Completely continuous movements in topological vector spaces

Published online by Cambridge University Press:  18 May 2009

J. H. Michael
J. H. Michael
Affiliation:
The University Glasgow
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Let A be a closed subset of a topological space X and f a continuous mapping of A into X with the following two properties:

1.1. f {Fr (A)} & f {Int (A)} are disjoint.

1.2. The mapping f* = f | Fr (A) is 1–1.

It is proved in [5], that if X is the euclidean n–sphere Sn = {x; x e Rn+1 and ― x ― = 1}, then

1.3. f {Fr(A)} = Fr {f(A)}.

[ Hence f{Int (A)} = Int {f(A)}].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 3 , December 1957 , pp. 135 - 141
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

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