Strong local homogeneity does not imply countable dense homogeneity

van Mill, Jan

doi:10.1090/S0002-9939-1982-0633296-0

Strong local homogeneity does not imply countable dense homogeneity
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by Jan van Mill

Proc. Amer. Math. Soc. 84 (1982), 143-148

DOI: https://doi.org/10.1090/S0002-9939-1982-0633296-0

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Abstract:

We give an example of a connected and locally connected subspace of the plane which is Baire and strongly locally homogeneous (as a consequence, the example is homogeneous) but which is not countable dense homogeneous.

References

R. D. Anderson, D. W. Curtis, and J. van Mill, A fake topological Hilbert space, Trans. Amer. Math. Soc. 272 (1982), no. 1, 311–321. MR 656491, DOI 10.1090/S0002-9947-1982-0656491-8
Ralph Bennett, Countable dense homogeneous spaces, Fund. Math. 74 (1972), no. 3, 189–194. MR 301711, DOI 10.4064/fm-74-3-189-194
Eric K. van Douwen, A compact space with a measure that knows which sets are homeomorphic, Adv. in Math. 52 (1984), no. 1, 1–33. MR 742164, DOI 10.1016/0001-8708(84)90049-5
Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
J. de Groot, Groups represented by homeomorphism groups, Math. Ann. 138 (1959), 80–102. MR 119193, DOI 10.1007/BF01369667

Sur la puissance de l’ensemble des "nombres de dimension" de M. Fréchet

8

Contribution à la théorie des ensembles homéomorphes

6

Jan van Mill, Homogeneous subsets of the real line, Compositio Math. 46 (1982), no. 1, 3–13. MR 660152