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Homogeneous inverse limit spaces with nonregular covering maps as bonding maps


Authors: James T. Rogers and Jeffrey L. Tollefson
Journal: Proc. Amer. Math. Soc. 29 (1971), 417-420
MSC: Primary 54.25
DOI: https://doi.org/10.1090/S0002-9939-1971-0273561-5
MathSciNet review: 0273561
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Abstract: We construct counterexamples to the conjecture that, in an inverse sequence $ (X,f)$ of closed manifolds $ {X_n}$ with covering maps $ f_m^n:{X_n} \to {X_m}$ as bonding maps, if the inverse limit space is homogeneous, then there exists an integer m such that (for all $ n > m$) the covering map $ f_m^n:{X_n} \to {X_m}$ is regular.


References [Enhancements On Off] (What's this?)

  • [1] S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, Princeton, N. J., 1952. MR 14, 398. MR 0050886 (14:398b)
  • [2] M. C. McCord, Inverse limit sequences with covering maps as bonding maps, Trans. Amer. Math. Soc. 114 (1965), 197-209. MR 30 #3450. MR 0173237 (30:3450)
  • [3] J. T. Rogers, Jr. and J. L. Tollefson, Involutions on solenoidal spaces, Fund. Math. (to appear). MR 0296923 (45:5982)
  • [4] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)
  • [5] R. M. Schori, Inverse limits and homogeneity, Trans. Amer. Math. Soc. 124 (1966), 533-539. MR 33 #6574. MR 0198416 (33:6574)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0273561-5
Keywords: Inverse limits, weak solenoidal spaces, normal series, covering map, homogeneity
Article copyright: © Copyright 1971 American Mathematical Society

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