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Last-modified: 2010-09-18 (土) 13:52:58

Definition Edit

Let X be a topological space and let α and β be cardinal numbers.
A family imgtex.fcgi?%5bres=100%5d%7b$%5c%7bU_%5cxi:%5cxi%3c%5calpha%5c%7d$%7d%25.png of subsets of X is called locally < β (in X) if for every point x of X there is a neighborhood V of x such that imgtex.fcgi?%5bres=100%5d%7b$%7c%5c%7b%5cxi%3c%5calpha:V%5ccap%20U_%5calpha%5cneq%5cemptyset%5c%7d%7c%3c%5cbeta$%7d%25.png.
The space X is called pseudo-(α,β)-compact if no set of nonempty open subsets of X indexed by α is locally < β.

Remark Edit

Reference Edit

W. W. Comfort, Products of spaces with properties of pseudo-compactness type, Topology Proc. Vol.4 (1979) pp.51-65.