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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
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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

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