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Lifting paths on quotient spaces |
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| Authors: | D Daniel J Nikiel ED Tymchatyn |
| Institution: | a Lamar University, Department of Mathematics, Beaumont, TX 77710, USA b Opole University, Institute of Mathematics and Informatics, ul. Oleska 48, 45-052 Opole, Poland c Texas A&M University, Department of Mathematics, College Station, TX 77843, USA d Nipissing University, Faculty of Arts and Sciences, North Bay, Ontario P1B 8L7, Canada e University of Saskatchewan, Department of Mathematics, Saskatoon, Saskatchewan S7N 0W0, Canada |
| Abstract: | Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X/G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn-Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g∈G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the first named author in a number of ways. |
| Keywords: | primary 54F15 secondary 54C05 54F05 54F50 |
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