When hereditarily collectionwise Hausdorffness implies regularity
- 1.6k Downloads
Every collectionwise Hausdorff (CWT2) first countable space is regular. Generalizations of first countability are considered. If X is hereditarily CWT2(HCWT2), blobular, of character N1, and contains no first countable S space, then X is regular. The existence of a first countable S space implies the existence of a nonregular, HCWT2, lob space of character N1. If it is consistent that there are no HCWT2 analogues of S spaces for all regular ordinals τ, then the following is consistent. Every HCWT2 globular space is regular.
AMS (MOS) subject classification (1980)Primary 54A25 54D10 54D15 Secondary 54A35 54E99 Key words and phases Hereditarily collectionwise Hausdorff regularity lob blobular globular S space right separated scattered
Unable to display preview. Download preview PDF.
- [D]E. K. van Douwen, Remote points, Dissertationes Math., vol. 188, 1981.Google Scholar
- [N]P. J. Nyikos, Order-theoretic base axioms, in: G. M. Reed, ed., Surveys in General Topology, Academic Press, New York, 1980, 367–398.Google Scholar
- [P1]S. Purisch, The orderability and closed images of scattered spaces, to appear.Google Scholar
- [P2]S. Purisch, Monotonically normal scattered spaces, in preparation.Google Scholar