Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An example concerning continuous selections of infinite-dimensional spaces


Author: Carl P. Pixley
Journal: Proc. Amer. Math. Soc. 43 (1974), 237-244
MSC: Primary 54C65
DOI: https://doi.org/10.1090/S0002-9939-1974-0328858-X
MathSciNet review: 0328858
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper shows that the conclusion of E. Michael's Selection Theorem 1.2 [Continuous selections. II, Ann. of Math. (2) 64 (1956), 562-580. MR 18, 325.] does not necessarily hold if the hypotheses are modified by dropping the assumption that the domain of the lsc carrier is of finite dimension, and strengthening the equilocal and global mapping conditions on the collection of images under the carrier.


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

  • [1] K. Borsuk, Theory of retracts, Monografie Mat., Tom 44, PWN, Warsaw, 1967. MR 35 #7306. MR 0216473 (35:7306)
  • [2] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. MR 13, 373. MR 0044116 (13:373c)
  • [3] O. Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315-360. MR 14, 396; 1278. MR 0050875 (14:396b)
  • [4] S. Lefschetz, Topics in topology, Ann. of Math. Studies, no. 10, Princeton Univ. Press, Princeton, N.J., 1942 MR 4, 86. MR 0007094 (4:86a)
  • [5] E. Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361-382. MR 17, 990. MR 0077107 (17:990e)
  • [6] -, Continuous selections. II, Ann. of Math. (2) 64 (1956), 562-580. MR 18, 325. MR 0080909 (18:325e)
  • [7] -, Local properties of topological spaces, Duke Math. J. 21 (1954), 163-171. MR 15, 977. MR 0062424 (15:977c)
  • [8] -, Convex structures and continuous selections, Canad. J. Math. 11 (1959), 556-575. MR 22 #230. MR 0109344 (22:230)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C65

Retrieve articles in all journals with MSC: 54C65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328858-X
Keywords: Selection, lower semicontinuous, absolute extensor, Hilbert cube, infinite dimensional
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society