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Homotopy and Isotopy Properties of Topological Spaces

Published online by Cambridge University Press:  20 November 2018

Daniel H. Gottlieb
Daniel H. Gottlieb*
Affiliation:
University of Illinois, Urbana, Illinois
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In 1961, S. T. Hu published a paper (1) in which he discussed the desirability of discovering those topological properties which are preserved under homotopy and isotopy equivalences. In that paper he gave general tests in terms of weakly hereditary and hereditary topological properties for homotopy and isotopy properties.

In this paper, general tests for homotopy and isotopy properties in terms of weakly hereditary properties and of a class of properties which the author calls open properties are given. In the last sections, we shall show the strong role played by the notions of dimension and separating subsets in forming isotopy properties.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 561 - 571
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Hu, S. T., Homotopy and isotopy properties of topological spaces. Can. J. Math., 13 (1961), 167–176.Google Scholar
2. Hurewicz, W. and Wallman, H., Dimension theory (Princeton, 1941).Google Scholar
3. Gottlieb, Daniel H., Homotopy and isotopy properties, Dissertation, University of California at Los Angeles (1962).Google Scholar