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Differentiable decompositions of manifolds into totally $ C\sp{\infty }$-path disconnected subsets


Author: M. V. Mielke
Journal: Proc. Amer. Math. Soc. 78 (1980), 439-442
MSC: Primary 57R22; Secondary 54C05, 58D15
DOI: https://doi.org/10.1090/S0002-9939-1980-0553391-2
MathSciNet review: 553391
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Abstract: For $ {C^\infty }$-manifolds M, N, the set of all $ {C^s}$-maps $ M \to N$ with totally $ {C^\infty }$-path disconnected fibers is shown to be dense in the set of all $ {C^s}$-maps $ M \to N$, if $ \dim N > 0$.


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

  • [1] R. D. Anderson, On collections of pseudo-arcs, Bull. Amer. Math. Soc. 56 (1950), 350.
  • [2] J. Dieudonne, Foundations of modern analysis, Academic Press, New York, 1960. MR 0120319 (22:11074)
  • [3] W. Lewis and J. J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4 (1978), 209-222. MR 0482693 (58:2750)
  • [4] M. V. Mielke, Sectional representation of multitopological spaces relative to a family of smoothness categories, Illinois J. Math. 23 (1979), 58-70. MR 516570 (80g:57041)
  • [5] J. R. Munkres, Elementary differential topology, Ann. of Math. Studies, no. 54, Princeton, N. J., 1963. MR 0163320 (29:623)
  • [6] S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 0193578 (33:1797)
  • [7] G. S. Ungar, Fiber spaces with totally path disconnected fiber, Ann. of Math. Studies, no. 60, Princeton, N. J., 1960, pp. 235-240.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553391-2
Keywords: Continuous decomposition, differentiable decomposition, totally $ {C^s}$-path disconnected fiber
Article copyright: © Copyright 1980 American Mathematical Society

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