| Popis: |
A topological space X is uniquely homogeneous if for every a , b ∈ X , there is exactly one homeomorphism h : X → X such that h ( a ) = b . We say that X is strongly uniquely homogeneous if it is uniquely homogeneous and the only continuous functions f : X → X are homeomorphisms and constant functions. We show that if n ≥ 2 , then there is a strongly uniquely homogeneous subspace of R n , all of whose homeomorphisms are restrictions of isometries of R n (rigid motions if n is even). Using a similar construction, we show that if κ is an infinite cardinal, then there is a strongly uniquely homogeneous Hausdorff and completely regular space of cardinality 2 κ . |
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