Definition:Ultraconnected Space/Definition 2
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Definition
A topological space $T = \struct {S, \tau}$ is ultraconnected if and only if the closures of every distinct pair of elements of $S$ are not disjoint:
- $\forall x, y \in S: \set x^- \cap \set y^- \ne \O$
Also see
- Results about ultraconnected spaces can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness