Geodesic
On the Complete Invariance Property in Some Uncountable Products
Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 221-229

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DOI

We consider uncountable products of nontrivial compact, convex subsets of normed linear spaces. We show that these products do not have the complete invariance property i.e. they include a nonempty, closed subset which is not a fixed point set (i.e. the set of all fixed points) for any continuous mapping from the product into itself. In particular we give an answer to W.Weiss' question whether uncountable powers of the unit interval have the complete invariance property.
DOI : 10.4153/CMB-1992-032-5
Mots-clés : 54H25 
Koszmider, Piotr. On the Complete Invariance Property in Some Uncountable Products. Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 221-229. doi: 10.4153/CMB-1992-032-5
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     title = {On the {Complete} {Invariance} {Property} in {Some} {Uncountable} {Products}},
     journal = {Canadian mathematical bulletin},
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     year = {1992},
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     number = {2},
     doi = {10.4153/CMB-1992-032-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-032-5/}
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