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In [[mathematics]], connectedness is used to refer to various properties [[meaning]], in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a [[component]] (or connected component).

In [[mathematics]], connectedness is used to refer to various properties [[meaning]], in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a [[component]] (or connected component).

==Connectedness in topology==

==Connectedness in topology==

A [http://en.wikipedia.org/wiki/Topological_space topological space] is said to be connected if it is not the union of two disjoint nonempty open sets. A set is open if it contains no point lying on its boundary; thus, in an informal, [[intuitive]] sense, the [[fact]] that a [[space]] can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces.

A [http://en.wikipedia.org/wiki/Topological_space topological space] is said to be connected if it is not the union of two disjoint nonempty open sets. A set is open if it contains no point lying on its boundary; thus, in an informal, [[intuitive]] sense, the [[fact]] that a [[space]] can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces.