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)

 
 

 

Concerning completable Moore spaces


Author: G. M. Reed
Journal: Proc. Amer. Math. Soc. 36 (1972), 591-596
MSC: Primary 54E30
DOI: https://doi.org/10.1090/S0002-9939-1972-0309074-2
MathSciNet review: 0309074
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The author obtains a generalization of well-known theorems due to Younglove and Fitzpatrick concerning the existence of dense metrizable subspaces in complete and completable Moore spaces. Based on this result, a new class of noncompletable Moore spaces is presented. In particular, an example of a separable noncompletable Moore space is given.


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

  • [1] S. Armentrout, Completing Moore spaces, Topology Conference (Arizona State Univ., Tempe, Ariz., 1967), Arizona State Univ., Tempe, Ariz., 1968, pp. 22-35. MR 39 #2123. MR 0240778 (39:2123)
  • [2] B. Fitzpatrick, Jr., On dense subspaces of Moore spaces, Proc. Amer. Math. Soc. 16 (1965), 1324-1328. MR 32 #1663. MR 0184190 (32:1663)
  • [3] G. D. Creede, Embedding of complete Moore spaces, Proc. Amer. Math. Soc. 28 (1971), 609-612. MR 43 #1119. MR 0275362 (43:1119)
  • [4] R. L. Moore, A set of axioms for plane analysis situs, Fund. Math. 25 (1935), 13-28.
  • [5] -, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1962. MR 27 #709. MR 0150722 (27:709)
  • [6] J. W. Ott, Subsets of separable spaces, Doctoral Dissertation, Auburn University, Auburn, Ala., 1969. MR 0394585 (52:15386)
  • [7] C. Pixley and P. Roy, Uncompletable Moore spaces, Proc. Auburn Topology Conference, Auburn, Ala., 1969, pp. 75-85. MR 0397671 (53:1529)
  • [8] G. M. Reed, Concerning normality, metrizability and the Souslin property in subspaces of Moore spaces, General Topology and Appl. 1 (1971), 223-246. MR 0290330 (44:7514)
  • [9] J. H. Roberts, A property related to completeness, Bull. Amer. Math. Soc. 38 (1932), 835-838. MR 1562528
  • [10] M. E. Estill (Rudin), Concerning abstract spaces, Duke Math. J. 17 (1950), 317-327. MR 13, 148. MR 0042686 (13:148b)
  • [11] -, Separation in non-separable spaces, Duke Math. J. 18 (1951), 623-629. MR 13, 148. MR 0042687 (13:148c)
  • [12] J. N. Younglove, Concerning dense metric subspaces of non-metric spaces, Fund. Math. 48 (1959), 15-25. MR 22 #1878. MR 0111011 (22:1878)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E30

Retrieve articles in all journals with MSC: 54E30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0309074-2
Keywords: Moore space, completable, metrizable, separable
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society