Xll

For

theorems in optimal control theory, and fixed point theorems in

ematical economics, usually does not understand that he/she is

tially studying the same things. And the student is led to st

basic topology individually. (An exceptional event, which appa

had a crucial influence on my generation of Moscow mathema

and, undoubtedly, on my own mathematical education, was th

cial (i.e., nonobligatory) topology course given by D. B. Fuchs

Mechanics and Mathematics Department of Moscow State Uni

in 1976-77.)

For several years (in the late 80s and the early 90s), I g

formal introductory topology courses for undergraduates an

school students at specialized math schools. I would like to

the administration of the Independent University of Moscow

opportunity to give this course as part of the basic curriculum t

students in the second and third semesters in 1996.

I am also extremely grateful to V. V. Prasolov, who took do

lecture notes and carried out their initial editing, and to the d

of Phasis Publishers, V. V. Filippov, for his initiative and sup

their publication.

The lecture note origins of the book left a significant impr

its style. It contains very few detailed proofs; I tried to give as

illustrations as possible and to show what really occurs in top

not always explaining why it occurs. As a rule, only those

(or sketches of proofs) that are interesting per se and have imp

generalizations are presented.

In conclusion, here is a list of suggested references.

[1] J. W. Milnor, Topology from the differentiable viewpoin

University Press of Virginia, Charlottesville, VA, 1965; Pri

Univ. Press, Princeton, NJ, 1997.

[2] A. H. Wallace, Differential Topology, W. A. Benjamin

York, 1968.

[3] V. V. Prasolov, Intuitive Topology, American Mathem

Society, Providence, RI, 1995.

[4] C. Kosniowski, A First Course in Algebraic Topology,

bridge University Press, 1980.

For

theorems in optimal control theory, and fixed point theorems in

ematical economics, usually does not understand that he/she is

tially studying the same things. And the student is led to st

basic topology individually. (An exceptional event, which appa

had a crucial influence on my generation of Moscow mathema

and, undoubtedly, on my own mathematical education, was th

cial (i.e., nonobligatory) topology course given by D. B. Fuchs

Mechanics and Mathematics Department of Moscow State Uni

in 1976-77.)

For several years (in the late 80s and the early 90s), I g

formal introductory topology courses for undergraduates an

school students at specialized math schools. I would like to

the administration of the Independent University of Moscow

opportunity to give this course as part of the basic curriculum t

students in the second and third semesters in 1996.

I am also extremely grateful to V. V. Prasolov, who took do

lecture notes and carried out their initial editing, and to the d

of Phasis Publishers, V. V. Filippov, for his initiative and sup

their publication.

The lecture note origins of the book left a significant impr

its style. It contains very few detailed proofs; I tried to give as

illustrations as possible and to show what really occurs in top

not always explaining why it occurs. As a rule, only those

(or sketches of proofs) that are interesting per se and have imp

generalizations are presented.

In conclusion, here is a list of suggested references.

[1] J. W. Milnor, Topology from the differentiable viewpoin

University Press of Virginia, Charlottesville, VA, 1965; Pri

Univ. Press, Princeton, NJ, 1997.

[2] A. H. Wallace, Differential Topology, W. A. Benjamin

York, 1968.

[3] V. V. Prasolov, Intuitive Topology, American Mathem

Society, Providence, RI, 1995.

[4] C. Kosniowski, A First Course in Algebraic Topology,

bridge University Press, 1980.