Connectedness
link author: James Munkres (via WP:JWB)
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{{Main article|Connected space}} |
{{Main article|Connected space}} |
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A [[topological space]] is said to be ''[[connected space|connected]]'' if it is not the union of two [[disjoint sets|disjoint]] nonempty [[open set]]s.{{Cite book|title=Topology|last=Munkres|first=James|publisher=Pearson|year=2000|isbn=978-0131816299|pages=148}} A [[Set (mathematics)|set]] is open if it contains no point lying on its [[boundary (topology)|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 [[topological space]] is said to be ''[[connected space|connected]]'' if it is not the union of two [[disjoint sets|disjoint]] nonempty [[open set]]s.{{Cite book|title=Topology|last=Munkres|first=James|author-link=James Munkres|publisher=Pearson|year=2000|isbn=978-0131816299|pages=148}} A [[Set (mathematics)|set]] is open if it contains no point lying on its [[boundary (topology)|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. |
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==Other notions of connectedness== |
==Other notions of connectedness== |
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