Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-04T09:46:39.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Centered Bases, Nested Bases, and Completability of Aronszajn Spaces

Published online by Cambridge University Press:  20 November 2018

Thomas M. Phillips
Thomas M. Phillips*
Affiliation:
Auburn University, Auburn, Alabama
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Definition. [1] A base B for the topology of a space S is centered provided every perfectly decreasing filterbase F in B is regular and either F is free or F converges. A centered base which contains no free perfectly decreasing filterbase is said to be complete.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1331 - 1335
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Green, J. W., Moore-closed spaces, completeness and centered bases, Gen. Top. and Appl. 4 (1974), 297–313.Google Scholar
2. Green, J. W., Completion and semicompletion of Moore spaces, Pac. J. Math. 57 (1975), 153—165.Google Scholar
3. Nyikos, P. J., Some surprisng base properties in topology, Proc. Topology Conf. (Univ. of North Carolina, Charlotte, N.C.) (Academic Press, New York, 1974), 427–450.Google Scholar
4. Phillips, T. M., Some observations on semicompletable Moore spaces, Proc. Topology Conf. Ohio University, Athens, Ohio) (Academic Press, New York, 1977), 313–324.Google Scholar
5. Phillips, T. M., An example in Baire space embeddings, Notices Amer. Math. Soc. 2J+ (1977), A-264.Google Scholar
6. Phillips, T. M., Primitive extensions of Aronszajn spaces, to appear, Pac. J. Math.Google Scholar
7. Pixley, C. and Roy, P., Uncompletable Moore spaces, Proc. Topology Conf. (Auburn University, Auburn, Ala.) 1969, 75–85.Google Scholar
8. Reed, G. M., Concerning completable Moore spaces, Proc. Amer. Math. Soc. 36 (1972), 591–596.Google Scholar
9. Rudin, M. E., Concerning abstract spaces, Duke Math. J. 17 (1950), 317–327.Google Scholar
10. Rudin, M. E., Separation in non-separable spaces, Duke Math. J. 18 (1951), 623–629.Google Scholar
11. Wicke, H. H. and Worrell, J. M., Jr., Topological completeness in first countable Hausdorff spaces I, Fund. Math. 75 (1972), 209–222.Google Scholar
12. Wicke, H. H. and Worrell, J. M., The local implies global characteristic of primitive sequences, Proc. Topology Conf. Memphis State University, Memphis, Tenn. (Marcell Dekker, New York, 1976), 269–282.Google Scholar