Local degree of separability and invariance of domain
Author:
L. B. Treybig
Journal:
Proc. Amer. Math. Soc. 34 (1972), 273-279
MSC:
Primary 54A25
DOI:
https://doi.org/10.1090/S0002-9939-1972-0295278-4
MathSciNet review:
0295278
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In ${E^n}$ an invariance of domain theorem may be proved assuming the Jordan Brouwer Theorem. In this paper such a theorem is proved for various locally compact, connected, Hausdorff spaces which satisfy a certain local degree of separability property. An example shows the separability condition may not be removed. A second theorem yields additional information about homogeneous spaces which satisfy the hypotheses of the first theorem.
-
W. W. Babcock, On linearly ordered topological spaces, Dissertation, Tulane University, New Orleans, La., 1964.
- Marvin J. Greenberg, Lectures on algebraic topology, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0215295
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
- John Marshall Slye, Flat spaces for which the Jordan curve theorem holds true, Duke Math. J. 22 (1955), 143–151. MR 66644
- L. B. Treybig, Concerning homogeneity in totally ordered, connected topological space, Pacific J. Math. 13 (1963), 1417–1421. MR 159309
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25
Retrieve articles in all journals with MSC: 54A25
Additional Information
Keywords:
Invariance of domain,
local degree of separability,
homogeneous space
Article copyright:
© Copyright 1972
American Mathematical Society