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)

 
 

 

Adjunction spaces of monotonically normal spaces and spaces dominated by monotonically normal subsets


Author: Takuo Miwa
Journal: Proc. Amer. Math. Soc. 87 (1983), 536-538
MSC: Primary 54E20; Secondary 54B17, 54C55, 54D15
DOI: https://doi.org/10.1090/S0002-9939-1983-0684653-9
MathSciNet review: 684653
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we shall prove the following results: (1) the adjunction space of two monotonically normal spaces is also monotonically normal, (2) a topological space is monotonically normal if and only if it is dominated by a collection of monotonically normal subsets.


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

  • [1] C. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. MR 0188982 (32:6409)
  • [2] -, Four generalizations of stratifiable spaces, General Topology and its Relation to Modern Analysis and Algebra. III (Proc. Third Prague Topological Sympos., 1971), Academia, Prague, 1972, pp. 73-76. MR 0362245 (50:14687)
  • [3] -, A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211-214. MR 0324644 (48:2994)
  • [4] O. Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315-360. MR 0050875 (14:396b)
  • [5] R. W. Heath, D. J. Lutzer and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. MR 0372826 (51:9030)
  • [6] S. T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, Mich., 1965. MR 0181977 (31:6202)
  • [7] E. A. Michael, Continuous selection. I, Ann. of Math. (2) 63 (1956), 361-382. MR 0077107 (17:990e)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E20, 54B17, 54C55, 54D15

Retrieve articles in all journals with MSC: 54E20, 54B17, 54C55, 54D15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0684653-9
Keywords: Monotonically normal spaces, adjunction space, AR, ANR, AE, ANE, space dominated by subsets
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society