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)

 
 

 

Products of sequential spaces


Author: Yoshio Tanaka
Journal: Proc. Amer. Math. Soc. 54 (1976), 371-375
DOI: https://doi.org/10.1090/S0002-9939-1976-0397665-6
MathSciNet review: 0397665
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: S. P. Franklin introduced the notion of a sequential space and characterized such spaces as being precisely the quotient images of metric spaces.

In this paper we investigate a necessary and sufficient condition for the product of a first countable space with a sequential space to be sequential, and we consider the property ``sequential space'' in $ {X^\omega }$.


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

  • [1] A. V. Arhangel'skii, Mappings and spaces, Uspehi Mat. Nauk 21 (1966), no. 4 (130), 133-184 = Russian Math. Surveys 21 (1966), no. 4, 115-162. MR 37 #3534. MR 0227950 (37:3534)
  • [2] S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115. MR 31 #5184. MR 0180954 (31:5184)
  • [3] -, Spaces in which sequences suffice. II, Fund. Math. 61 (1967), 51-56. MR 36 #5882. MR 0222832 (36:5882)
  • [4] L. F. McAuley, A relation between perfect separability, completeness, and normality in semimetric spaces, Pacific J. Math. 6 (1956), 315-326. MR 18, 325. MR 0080907 (18:325c)
  • [5] E. A. Michael, $ {\aleph _0}$-spaces, J. Math. Mech. 15 (1966), 983-1002. MR 34 #6723. MR 0206907 (34:6723)
  • [6] -, A quintuple quotient quest, General Topology and Appl. 2 (1972), 91-138. MR 46 #8156. MR 0309045 (46:8156)
  • [7] J. Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272-284. MR 17, 994. MR 0077122 (17:994b)
  • [8] K. Morita, On spaces having the weak topology with respect to closed coverings, Proc. Japan Acad. 29 (1953), 537-543. MR 15, 977. MR 0062423 (15:977b)
  • [9] -, Some results on $ M$-spaces, Colloq. Math. Societatis János Bolyai 8, Topics in Topology, Keszthely, Hungary, 1972, pp. 489-503.
  • [10] S. Nedev, Symmetrizable spaces and final compactness, Dokl. Akad. Nauk SSSR 175 (1967), 532-534 = Soviet Math. Dokl. 8 (1967), 890-892. MR 35 #7293. MR 0216460 (35:7293)
  • [11] R. C. Olson, $ Bi$-quotient maps, countably $ bi$-sequential spaces, and related topics, General Topology and Appl. 4 (1974), 1-1t28. MR 0365463 (51:1715)
  • [12] F. Siwiec, Sequence-covering and countably $ bi$-quotient mappings, General Topology and Appl. 1 (1971), no. 2, 143-154. MR 44 #5933. MR 0288737 (44:5933)
  • [13] Y. Tanaka, On quasi-k-spaces, Proc. Japan Acad. 46 (1970), 1074-1079. MR 45 #5946. MR 0296887 (45:5946)
  • [14] -, On symmetric spaces, Proc. Japan Acad. 49 (1973), 106-111. MR 0328878 (48:7220)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0397665-6
Keywords: Sequential spaces, Fréchet spaces, strongly Fréchet spaces, symmetrizable spaces, semimetrizable spaces
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society