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Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
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Introduction to Differential and Algebraic Topology (Paperback, Softcover reprint of hardcover 1st ed. 1995)
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Introduction to Differential and Algebraic Topology (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Series: Texts in the Mathematical Sciences, 9
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Topology as a subject, in our opinion, plays a central role in
university education. It is not really possible to design courses
in differential geometry, mathematical analysis, differential
equations, mechanics, functional analysis that correspond to the
temporary state of these disciplines without involving topological
concepts. Therefore, it is essential to acquaint students with topo
logical research methods already in the first university courses.
This textbook is one possible version of an introductory course in
topo logy and elements of differential geometry, and it absolutely
reflects both the authors' personal preferences and experience as
lecturers and researchers. It deals with those areas of topology
and geometry that are most closely related to fundamental courses
in general mathematics. The educational material leaves a lecturer
a free choice in designing his own course or his own seminar. We
draw attention to a number of particularities in our book. The
first chap ter, according to the authors' intention, should
acquaint readers with topolo gical problems and concepts which
arise from problems in geometry, analysis, and physics. Here,
general topology (Ch. 2) is presented by introducing con
structions, for example, related to the concept of quotient spaces,
much earlier than various other notions of general topology thus
making it possible for students to study important examples of
manifolds (two-dimensional surfaces, projective spaces, orbit
spaces, etc.) as topological spaces, immediately."
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