Hanner's theorem

The set of Hanner is a mathematical theorem from the branch of topology , which the Swedish mathematician Olof Hanner back. The sentence deals with an important property of absolute surrounding retracts .

Formulation of the sentence

The sentence can be formulated as follows:

If a topological space of a finite number of open compartments covers , all of which are absolute Umgebungsretrakte so is itself an absolute Umgebungsretrakt. ${\displaystyle X}$ ${\displaystyle X}$

Corollary

Due to the fact that the and thus all of its open subsets are absolute surrounding retracts, Hanner's theorem immediately leads to the following theorem: ${\displaystyle \mathbb {R} ^{n}\;(n\in \mathbb {N} )}$

Every compact topological manifold is an absolute surrounding retract.

literature

• Horst Schubert : Topology . 4th edition. BG Teubner Verlag , Stuttgart 1975, ISBN 3-519-12200-6 . MR0423277

References and footnotes

1. ↑ ^{a b c} Horst Schubert: Topology. 1975, pp. 158-160