Hostname: page-component-7bb8b95d7b-pwrkn Total loading time: 0 Render date: 2024-10-01T11:37:33.595Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on bounds of cardinal functions in the closed preimage

Published online by Cambridge University Press:  17 April 2009

Edward S. Miller
Edward S. Miller
Affiliation:
Division of Natural Sciences, Lewis-Clark State College, Lewiston ID 83501, United States of America
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.

Let X and Y be T1 spaces and f: X → Y be a closed and onto mapping. If a fiber of the mapping f is defined to be the inverse image of a singleton in the range, then a bound for the tightness of the domain is the product of the tightness of the range and the supremum of the tightness of the fibers of f. Similar bounds can also be shown for the Lindelöf degree and the extent of X. Examples are provided to demonstrate that such results are not possible for open maps. Cellularity and spread are discussed briefly.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 69 - 74
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Hodel, R., ‘Cardinal functions I’, in Handbook of Set-Theoretic Topology (Elsevier Science Publishers, B.V, 1984), pp. 1–62.Google Scholar
[2]Kunen, K., Set theory (Elsevier Science Publishers, B.V, 1980).Google Scholar
[3]Sakai, M., ‘A new class of isocompact spaces and related results’, Pacific J. Math. 122 (1986), 211–221.CrossRefGoogle Scholar
[4]Todorčević, S., ‘Remarks on cellularity in products’, Compositio Math. 57 (1986), 357–372.Google Scholar