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hyperconnected space∗ yark† 2013-03-21 17:22:44 A topological space X is said to be hyperconnected if no pair of nonempty open sets of X is disjoint (or, equivalently, if X is not the union of two proper closed sets). Hyperconnected spaces are sometimes known as irreducible sets. All hyperconnected spaces are connected, locally connected, and pseudocompact. Any infinite set with the cofinite topology is an example of a hyperconnected space. Similarly, any uncountable set with the cocountable topology is hyperconnected. Affine spaces and projectives spaces over an infinite field, when endowed with the Zariski topology, are also hyperconnected. ∗ hHyperconnectedSpacei created: h2013-03-21i by: hyarki version: h35813i Privacy setting: h1i hDefinitioni h54D05i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
