Jan van Mill
نویسنده
چکیده
De Groot proved that every group is the autohomeomorphism group of some metrizable space. A space is totally disconnected if every connected subset of it contains at most one point. We prove that every separable metrizable totally disconnected topological group is topologically isomorphic to the autohomeomorphism group of some separable metrizable space, when given the compact-open topology. It is known that, for example, the circle group cannot be realized in this way.
منابع مشابه
Guram Bezhanishvili , Nick Bezhanishvili , Joel Lucero - Bryan and Jan van Mill S 4 . 3 and hereditarily extremally disconnected spaces
Research Article Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan and Jan van Mill S4.3 and hereditarily extremally disconnected spaces Abstract: Themodal logic S4.3 de nes the class of hereditarily extremally disconnected spaces (HED-spaces). We construct a countable HED-subspaceX of the Gleason cover of the real closed unit interval [0, 1] such that S4.3 is the logic ofX.
متن کاملTopology Proceedings 33 (2009) pp. 153-161: Homogeneous spaces and transitive actions by $\aleph_0$-bounded groups
We construct a homogeneous connected Polish space X on which no א0-bounded topological group acts transitively. In fact, X is homeomorphic to a convex subset of Hilbert space `.
متن کاملHomeomorphism Groups and Metrisation of Manifolds
We prove that a manifold M is metrisable if and only if its group of homeomorphisms H (M) endowed with the compact-open topology is a qspace. We also discuss pseudo-character and tightness. All spaces under discussion are Tychonoff.
متن کامل