Algebraic Topology A Computational Approach - Kaczynski , Mischaikow , Mrozek
T Kaczynski
Universit e de Sherbro o ke
K Mischaikow
Georgia Institute of Technology
M Mrozek
Jagellonian University
April 18/2000
The subject of Topology grew out of the foundations of calculus and more
generally analysis If you took a typical calculus sequence then you began by
learningabout functionsof the realline The focus was ondi erentiablefunc
tions and how they can be best approximated locally by linear functions the
derivative Along the way you learned about continuous functions Again
the emphasis was on local properties such as limits a notable exception is
the intermediate value theorem Later on these concepts were generalized to
functions of more than one variable i e functions from Rn to Rm Topology
incorporates further generalizations In particular it allows one to study the
local and global properties of continuous functions between general spaces
Universit e de Sherbro o ke
K Mischaikow
Georgia Institute of Technology
M Mrozek
Jagellonian University
April 18/2000
The subject of Topology grew out of the foundations of calculus and more
generally analysis If you took a typical calculus sequence then you began by
learningabout functionsof the realline The focus was ondi erentiablefunc
tions and how they can be best approximated locally by linear functions the
derivative Along the way you learned about continuous functions Again
the emphasis was on local properties such as limits a notable exception is
the intermediate value theorem Later on these concepts were generalized to
functions of more than one variable i e functions from Rn to Rm Topology
incorporates further generalizations In particular it allows one to study the
local and global properties of continuous functions between general spaces
