Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-09T05:10:03.838Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

Kelley, J. L., General topology (New York, 1955).Google Scholar
Lefschetz, S., Algebraic topology Amer. Math. Soc. Colloquium Publications, 27 (1942).Google Scholar
Leray, J., La théorie des points fixes et ses applications en analyse, Rend. Sem. Mat., 15 (1955–1956), 65–74.Google Scholar
Leray, J., AND Schauder, J., Topologie et Equations fonctionelles, Ann. Sci. ificole Norm.Sup. 51 (1934), 45–78.CrossRefGoogle Scholar
Michael, J. H., Continuous mappings of subsets of the euclidean n-sphere, Bull. Acad. Polon. Sci., 5 (1957), 133–137.Google Scholar
Nagumo, Mitio, Degree of mapping in convex linear topological spaces, Amer. J. Math. 73 (1951), 497–511.CrossRefGoogle Scholar