A compact group which is not Valdivia compact |
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| Authors: | Wieslaw Kubis Vladimir Uspenskij |
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| Institution: | Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland ; Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701 |
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| Abstract: | A compact space  is Valdivia compact if it can be embedded in a Tikhonov cube  in such a way that the intersection  is dense in  , where  is the sigma-product ( the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight  which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps. |
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| Keywords: | Valdivia compact space open map retract indecomposable group |
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