Top > super-Valdivia compact
HTML convert time to 0.136 sec.

# super-Valdivia compact

Last-modified: 2010-12-17 (¶â) 22:26:41

## Definition

• Compact Hausdorff space X is a super-Valdivia compact space if each x \in X is contained in some dense ¦²-subset of X

## Property

• Let f:X¢ªY be a continuous open surjection between compact Hausdorff spaces. Suppose, moreover, that Y has a dense set of G_¦Ä points. If X is super-Valdivia , then Y is Corson.
• Let X and Y be nonempty compact Hausdorff spaces such that X has a dense set of G_¦Ä points and X¡ßY is super-Valdivia compact, then X is Corson and Y super-Valdivia.
• Let X_a, a \in ¦« be an arbitrary family of nonempty compact Hausdorff spaces such that each X_a has a dense subset of G_¦Ä points. Then the follwing two conditions are equivalent.
1. ¦°_{a \in ¦«} X_a is super-Valdivia compact.
2. X_a is a Corson compact for every a \in ¦«.

## Reference

Kalenda, Ondřej(CZ-KARLMP-MA),A characterization of Valdivia compact spaces, (English summary)Collect. Math. 51 (2000), no. 1, 59--81.