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

Miwa, Takuo

doi:10.1090/S0002-9939-1983-0684653-9

Adjunction spaces of monotonically normal spaces and spaces dominated by monotonically normal subsets
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Proc. Amer. Math. Soc. 87 (1983), 536-538 Request permission

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

Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982
C. R. Borges, Four generalizations of stratifiable spaces, General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971) Academia, Prague, 1972, pp. 73–76. MR 0362245
Carlos R. Borges, A study of monotonically normal spaces, Proc. Amer. Math. Soc. 38 (1973), 211–214. MR 324644, DOI 10.1090/S0002-9939-1973-0324644-4
Olof Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315–360. MR 50875, DOI 10.1007/BF02591501
R. W. Heath, D. J. Lutzer, and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481–493. MR 372826, DOI 10.1090/S0002-9947-1973-0372826-2
Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
Ernest Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361–382. MR 77107, DOI 10.2307/1969615