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# ultraconnected space

A topological space $X$ is said to be ultraconnected if no pair of nonempty closed sets of $X$ is disjoint.

All ultraconnected spaces are path-connected, normal, limit point compact, and pseudocompact.

Defines:

ultraconnected, ultra-connected

Related:

Hyperconnected

Synonym:

ultra-connected space

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54D05*no label found*

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Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz