Connected im Kleinen

The expression im kleinen is German and means "on a small scale." A topological space is connected im kleinen at a point x if every neighborhood U of x contains an open neighborhood V of x such that any two points of V lie in some connected subset of U.

A locally connected space is connected im kleinen, but the converse is false, as can be demonstrated by the broom space.

See also

Broom Space, Connected

This entry contributed by Margherita Barile

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Willard, S. General Topology. Reading, MA: Addison-Wesley, p. 201, 1970.

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Connected im Kleinen

Cite this as:

Barile, Margherita. "Connected im Kleinen." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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