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)

 
 

 

Spaces defined by sequences


Author: Andrew J. Berner
Journal: Proc. Amer. Math. Soc. 55 (1976), 193-200
DOI: https://doi.org/10.1090/S0002-9939-1976-0394573-1
MathSciNet review: 0394573
Full-text PDF

Abstract | References | Additional Information

Abstract: The biquotient, countably biquotient, hereditarily quotient, and quotient images of $ q$-spaces are classified. Also, the quotient images of paracompact $ M$-spaces, and the quotient images of $ M$-spaces are classified without any separation axioms. New definitions are given for certain familiar classes of spaces to give the definitions more uniformity.


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

  • [1] E. A. Michael, A quintuple quotient quest, General Topology and Appl. 2(1972), 91-138. MR46 #8156. MR 0309045 (46:8156)
  • [2] -, A note on closed maps and compact sets, Israel J. Math. 2(1964), 173-176. MR31 #1659. MR 0177396 (31:1659)
  • [3] -, Bi-quotient maps and Cartesian products of quotient maps, Ann. Inst. Fourier (Grenoble) 18(1968), fasc. 2, 287-302(1969). MR39 #6277. MR 0244964 (39:6277)
  • [4] -, On representing spaces as images of metrizable and related spaces, General Topology and Appl. 1(1971), 329-343. MR45 #2681. MR 0293604 (45:2681)
  • [5] J. Nagata, Quotient and bi-quotient spaces of $ M$-spaces, Proc. Japan Acad. 45(1969), 25-29. MR39 #6278. MR 0244965 (39:6278)
  • [6] R. C. Olson, Bi-quotient maps, countably bi-sequential spaces and related topics, General Topology and Appl. 4(1974), 1-28. MR 0365463 (51:1715)
  • [7] F. Siwiec, Sequence-covering and countably bi-quotient mappings, General Topology and Appl. 1(1971), no. 2, 143-154. MR44 #5933. MR 0288737 (44:5933)
  • [8] H. H. Wicke, On the Hausdorff open continuous images of Hausdorff paracompact $ p$-spaces, Proc. Amer. Math. Soc. 22(1969), 136-140. MR39 #4801. MR 0243480 (39:4801)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394573-1
Keywords: Quotient map, biquotient map, hereditarily quotient map, $ k$-space, $ q$-space, relatively bi-quasi-$ k$-space, $ M$-space, pointwise countable type, strict $ q$-space
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society