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Connected space

Ciro Santilli (@cirosantilli, 37) Mathematics Area of mathematics Calculus Topology
Updated 2025-07-16  1 By others on same topic  0 Discussions Create my own version
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    • Connected component Connected space
    • Simply connected space Connected space
      • Loop (topology) Simply connected space

Connected component

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Connected space
When a disconnected space is made up of several smaller connected spaces, then each smaller component is called a "connected component" of the larger space.
See for example the

Simply connected space

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Connected space

Loop (topology)

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Simply connected space

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Connected space by Wikipedia Bot 0
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In topology, a connected space is a fundamental concept that refers to a topological space that cannot be divided into two disjoint, non-empty open sets. More formally, a topological space \( X \) is called connected if there do not exist two open sets \( U \) and \( V \) such that: 1. \( U \cap V = \emptyset \) 2. \( U \cup V = X \) 3.
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