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On the semi-canonical property in the product space $ X\times I$


Authors: A. Okuyama and Y. Yasui
Journal: Proc. Amer. Math. Soc. 68 (1978), 229-234
MSC: Primary 54E99
DOI: https://doi.org/10.1090/S0002-9939-1978-0474223-8
MathSciNet review: 0474223
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Abstract: As one of the several properties in generalized metric spaces, the semi-canonical property has been discussed from the viewpoint of the extension of mappings. In this paper, that property will be discussed in product space $ X \times I$ and reduced to a property of X.


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

  • [1] A. V. Arhangel'skiĭ, Bicompact sets and the topology of spaces, Trudy Moskov. Mat. Obšč. 13 (1965), 3-55 = Trans. Moscow Math. Soc. 13 (1965), 1-62. MR 0195046 (33:3251)
  • [2] C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16. MR 0188982 (32:6409)
  • [3] M. R. Cauty, Une généralisation du théorème de Borsuk-Whitehead-Hanner aux espaces stratifiables, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A271-A274. MR 0309058 (46:8169)
  • [4] J. G. Ceder, Some generalizations of a metric space, Pacific J. Math. 11 (1961), 105-126. MR 0131860 (24:A1707)
  • [5] M. M. Čoban, Perfect mappings and spaces of countable type, Vestnik Moskov. Univ. Ser. I Mat. Meh. 22 (1967), no. 6, 87-93. MR 0220247 (36:3313)
  • [6] D. M. Hyman, A generalization of the Borsuk-Whitehead-Hanner theorem, Pacific J. Math. 23 (1967), 263-271. MR 0225295 (37:889)
  • [7] D. M. Hyman, A note on closed maps and metrizability, Proc. Amer. Math. Soc. 21 (1969), 109-112. MR 0238258 (38:6534)
  • [8] N. Lasnev, Closed images of metric spaces, Dokl. Akad. Nauk SSSR 170 (1966) = Soviet Math. Dokl. 7 (1966), 1219-1221. MR 0203698 (34:3547)
  • [9] E. Michael and K. Nagami, Compact-covering images of metric spaces, Proc. Amer. Math. Soc. 37 (1973), 260-266. MR 0307148 (46:6269)
  • [10] K. Morita, On the simple extension of a space with respect to a uniformity. IV, Proc. Japan Acad. 27 (1951), 632-636. MR 0052090 (14:571e)
  • [11] S. San-ou, A note on $ \Xi $-product, J. Math. Soc. Japan 29 (1977), 281-285. MR 0442894 (56:1269)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0474223-8
Keywords: Semi-canonical cover, semi-canonical pair, $ {M_1}$-space, metric space, compact-covering map, open map, X-base, countable character, first countable space
Article copyright: © Copyright 1978 American Mathematical Society

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