Each homogeneous nondegenerate chainable continuum is a coset space.
نویسندگان
چکیده
منابع مشابه
Each Homogeneous Nondegenerate Chainable Continuum Is a Coset Space
Let A" be a compact Hausdorff homogeneous space and G be the full group of homeomorphisms from X to X. We denote the isotropy group at x by Gx. If G is topologized by uniform convergence [l], then it is well known that G is a topological group, and the function 6: G/GX—*X, defined by 6{gGx)=g{x) is one-one and continuous. It is an open problem whether ô is a homeomorphism, i.e., whether X is a ...
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In the first two volumes of Fundamenta Mathematica, Knaster and Kuratowski raised the following two questions [15], [16]: (1) If a nondegenerate, bounded plane continuum is homogeneous, is it necessarily a simple closed curve? (2) Does there exist a continuum each subcontinuum of which is indecomposable? Although Knaster settled the second question in 1922 [14], it was to remain until 1948 for ...
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This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a nondegenerate chainable continuum. This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum. By R.H. Bing’s theorem eleven [2] if a metric continuum X contains a non-degenerate subconti...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1961
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1961-0126505-4