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.
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 EditInsall Matt Unicoherent Space MathWorld 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 580104711, wikipedia, wiki, book, books, library,
