Unicoherent

﻿
Unicoherent

A topological space $X$ is said to be unicoherent if it is connected and the following property holds:

For any closed, connected $A, B subset X$ with $X=A cup B$, the intersection $A cap B$ is connected.

For example, any closed interval on the real line is unicoherent, but a circle is not.

References

*MathWorld|urlname=UnicoherentSpace|title=Unicoherent Space|author=Insall, Matt

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Dendroid (topology) — In topology, a hereditarily unicoherent, arcwise connected continuum is called a dendroid. A continuum X is called hereditarily unicoherent if every subcontinuum of X is unicoherent. A locally connected dendroid is called a dendrite. This… …   Wikipedia

• List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …   Wikipedia

• Simply connected space — In topology, a topological space is called simply connected (or 1 connected) if it is path connected and every path between two points can be continuously transformed, staying within the space, into any other path while preserving the two… …   Wikipedia

• List of mathematics articles (U) — NOTOC U U duality U quadratic distribution U statistic UCT Mathematics Competition Ugly duckling theorem Ulam numbers Ulam spiral Ultraconnected space Ultrafilter Ultrafinitism Ultrahyperbolic wave equation Ultralimit Ultrametric space… …   Wikipedia