Decompositions of rigid spaces
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- by Fons van Engelen and Jan van Mill
- Proc. Amer. Math. Soc. 89 (1983), 533-536
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715881-1
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Abstract:
We give an example of a rigid subspace of ${\mathbf {R}}$ which can be decomposed into two homeomorphic homogeneous parts, and of a rigid subspace of ${\mathbf {R}}$ which can be decomposed into two homeomorphic rigid parts.References
- Fons van Engelen, Homogeneous Borel sets of ambiguous class two, Trans. Amer. Math. Soc. 290 (1985), no. 1, 1–39. MR 787953, DOI 10.1090/S0002-9947-1985-0787953-3 M. Lavrentieff, Contribution à la théorie des ensembles homéomorphes, Fund. Math. 6 (1924), 149-160. J. Menu, A partition of ${\mathbf {R}}$ in two homogeneous and homeomorphic parts (to appear).
- Jan van Mill, Strong local homogeneity does not imply countable dense homogeneity, Proc. Amer. Math. Soc. 84 (1982), no. 1, 143–148. MR 633296, DOI 10.1090/S0002-9939-1982-0633296-0
- Jan van Mill, Homogeneous subsets of the real line, Compositio Math. 46 (1982), no. 1, 3–13. MR 660152
- Jan van Mill and Evert Wattel, Partitioning spaces into homeomorphic rigid parts, Colloq. Math. 50 (1985), no. 1, 95–102. MR 818090, DOI 10.4064/cm-50-1-95-102
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 533-536
- MSC: Primary 54G20; Secondary 54C99
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715881-1
- MathSciNet review: 715881