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ladder connected (Definition)

Definition Suppose $ X$ is a topological space. Then $ X$ is called ladder connected provided that any open cover $ \mathcal{U}$ of $ X$ has the following property: If $ p,q\in X$, then there exists a finite number of open sets $ U_1,\ldots, U_N$ from $ \mathcal{U}$ such that $ p\in U_1$, $ U_1\cap U_2\neq \emptyset$, $ \ldots$ , $ U_{N-1}\cap U_N\neq\emptyset$, and $ q\in U_N$.



"ladder connected" is owned by mathcam. [ full author list (2) | owner history (2) ]
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See Also: characterization of connected compact metric spaces.
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Cross-references: open sets, finite, property, open cover, topological space

This is version 3 of ladder connected, born on 2003-10-15, modified 2003-12-06.
Object id is 4867, canonical name is LadderConnected.
Accessed 1077 times total.

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AMS MSC: 54-00 (General topology :: General reference works )
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