This book is a course in general topology, intended for students in
the first year of the second cycle (in other words, students in
their third univer sity year). The course was taught during the
first semester of the 1979-80 academic year (three hours a week of
lecture, four hours a week of guided work). Topology is the study
of the notions of limit and continuity and thus is, in principle,
very ancient. However, we shall limit ourselves to the origins of
the theory since the nineteenth century. One of the sources of
topology is the effort to clarify the theory of real-valued
functions of a real variable: uniform continuity, uniform
convergence, equicontinuity, Bolzano-Weierstrass theorem (this work
is historically inseparable from the attempts to define with
precision what the real numbers are). Cauchy was one of the
pioneers in this direction, but the errors that slip into his work
prove how hard it was to isolate the right concepts. Cantor came
along a bit later; his researches into trigonometric series led him
to study in detail sets of points of R (whence the concepts of open
set and closed set in R, which in his work are intermingled with
much subtler concepts). The foregoing alone does not justify the
very general framework in which this course is set. The fact is
that the concepts mentioned above have shown themselves to be
useful for objects other than the real numbers."
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Undergraduate Texts in Mathematics |
| Release date: |
July 1984 |
| First published: |
August 1984 |
| Translators: |
S.K. Berberian
|
| Authors: |
J. Dixmier
|
| Dimensions: |
235 x 155 x 16mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
141 |
| Edition: |
1984 ed. |
| ISBN-13: |
978-0-387-90972-1 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
Promotions
|
| LSN: |
0-387-90972-9 |
| Barcode: |
9780387909721 |
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