 TOPICS  # Disconnected Space

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space with more than one connected component.

A subset of the Euclidean plane with more than one element can always be disconnected by cutting it through with a line (i.e., by taking out its intersection with a suitable straight line). In fact, it is certainly possible to find a line such that two points of lie on different sides of . If the Cartesian equation of is (1)

for fixed real numbers , then the set is disconnected, since it is the union of the two nonempty open subsets (2)

and (3)

which are the sets of elements of lying on the two sides of .

Totally Disconnected Space

This entry contributed by Margherita Barile

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## Cite this as:

Barile, Margherita. "Disconnected Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DisconnectedSpace.html