Properties
The Euler characteristic of any closed odd-dimensional manifold is zero. The case for orientable examples is a corollary of Poincaré duality. This property applies more generally to any compact stratified space all of whose strata are odd-dimensional. Furthermore, the Euler characteristic behaves well with respect to many basic operations on topological spaces, as follows.
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Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)