In mathematics, the caliber or calibre of a topological space X is a cardinal κ such that for every set of κ nonempty open subsets of X there is some point of X contained in κ of these subsets. This concept was introduced by Shanin (1948).
There is a similar concept for posets. A pre-caliber of a poset P is a cardinal κ such that for any collection of elements of P indexed by κ, there is a subcollection of cardinality κ that is centered. Here a subset of a poset is called centered if for any finite subset there is an element of the poset less than or equal to all of them.
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References
- Kunen, Kenneth (2011), Set theory, Studies in Logic, vol. 34, London: College Publications, ISBN 978-1-84890-050-9, MR 2905394, Zbl 1262.03001
- Shanin, N. A. (1948), "On the product of topological spaces", Trudy Mat. Inst. Steklov., 24, MR 0027310
This page was last edited on 12 August 2014, at 18:49