from algebric topology

موضوع: from algebric topology الجمعة ماي 16, 2008 5:17 pm

Some useful notions from algebraic topology
See also list of algebraic topology topics.

Homology and cohomology: Betti numbers, Euler characteristic.
Intuitively-attractive applications: Brouwer fixed-point theorem, Hairy ball theorem, Borsuk-Ulam theorem, Ham sandwich theorem.
Homotopy groups (including the fundamental group).
Chern classes, Stiefel-Whitney classes, Pontryagin classes.

[edit] Generalizations

Occasionally, one needs to use the tools of topology but a "set of points" is not available. In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.

[edit] Topology in Works of Art and Literature

Some M. C. Escher works illustrate topological concepts, such as Möbius strips and non-orientable spaces.
Both Philip K. Dick's A Scanner Darkly and Robert Anton Wilson's Schrodinger's Cat trilogy reference topological ideas.

_________________
واخر دعوانا أن الحمد لله رب العالمين

موضوع: رد: from algebric topology السبت ماي 17, 2008 4:44 pm

thank's alot shady
u r very strong in your topics
_________________