In mathematics, a unicoherent space is a topological space that is connected and in which the following property holds:
For any closed, connected with , the intersection is connected.
For example, any closed interval on the real line is unicoherent, but a circle is not.
If a unicoherent space is more strongly hereditarily unicoherent (meaning that every subcontinuum is unicoherent) and arcwise connected, then it is called a dendroid. If in addition it is locally connected then it is called a dendrite. The Phragmen–Brouwer theorem states that, for locally connected spaces, unicoherence is equivalent to a separation property of the closed sets of the space.
Referencesedit
Charatonik, Janusz J. (2003). "Unicoherence and Multicoherence". Encyclopedia of General Topology. pp. 331–333. doi:10.1016/B978-044450355-8/50088-X. ISBN9780444503558.
unicoherent, space, mathematics, unicoherent, space, topological, space, displaystyle, that, connected, which, following, property, holds, closed, connected, displaystyle, subset, with, displaystyle, intersection, displaystyle, connected, example, closed, inte. In mathematics a unicoherent space is a topological space X displaystyle X that is connected and in which the following property holds For any closed connected A B X displaystyle A B subset X with X A B displaystyle X A cup B the intersection A B displaystyle A cap B is connected For example any closed interval on the real line is unicoherent but a circle is not If a unicoherent space is more strongly hereditarily unicoherent meaning that every subcontinuum is unicoherent and arcwise connected then it is called a dendroid If in addition it is locally connected then it is called a dendrite The Phragmen Brouwer theorem states that for locally connected spaces unicoherence is equivalent to a separation property of the closed sets of the space References editCharatonik Janusz J 2003 Unicoherence and Multicoherence Encyclopedia of General Topology pp 331 333 doi 10 1016 B978 044450355 8 50088 X ISBN 9780444503558 External links editInsall Matt Unicoherent Space MathWorld nbsp This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Unicoherent space amp oldid 1158921485, wikipedia, wiki, book, books, library,