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- Q1673182 subject Q8797713.
- Q1673182 abstract "Template:ForIn mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two proper closed sets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are equivalent: No two nonempty open sets are disjoint. X cannot be written as the union of two proper closed sets. Every nonempty open set is dense in X. The interior of every proper closed set is empty.A space which satisfies any one of these conditions is called hyperconnected or irreducible.An irreducible set is a subset of a topological space for which the subspace topology is irreducible. Some authors do not consider the empty set to be irreducible (even though it vacuously satisfies the above conditions).".
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- Q1673182 wikiPageWikiLink Q8797713.
- Q1673182 comment "Template:ForIn mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two proper closed sets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are equivalent: No two nonempty open sets are disjoint. X cannot be written as the union of two proper closed sets. Every nonempty open set is dense in X.".
- Q1673182 label "Hyperconnected space".