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Titlebook: General Topology; Jacques Dixmier Textbook 1984 Springer Science+Business Media New York 1984 Cantor.Compact space.Connected space.Finite.

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發(fā)表于 2025-3-21 19:09:43 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱General Topology
編輯Jacques Dixmier
視頻videohttp://file.papertrans.cn/383/382142/382142.mp4
叢書名稱Undergraduate Texts in Mathematics
圖書封面Titlebook: General Topology;  Jacques Dixmier Textbook 1984 Springer Science+Business Media New York 1984 Cantor.Compact space.Connected space.Finite.
描述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 foregoi
出版日期Textbook 1984
關(guān)鍵詞Cantor; Compact space; Connected space; Finite; Topology; function; theorem; variable
版次1
doihttps://doi.org/10.1007/978-1-4757-4032-5
isbn_softcover978-1-4419-2823-8
isbn_ebook978-1-4757-4032-5Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer Science+Business Media New York 1984
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 20:30:57 | 只看該作者
板凳
發(fā)表于 2025-3-22 00:53:52 | 只看該作者
Constructions of Topological Spaces, seen this in the study of vector space structure. The same is true for topological spaces. This yields important new spaces (for example, the tori ..; cf. also the projective spaces, in the exercises for Chapter IV).
地板
發(fā)表于 2025-3-22 08:14:40 | 只看該作者
Compact Spaces,uitful definition (see the properties of compact spaces in §§2 and 3, and the applications in nearly all the rest of the course). In §4, we adjoin to the real line . a point + ∞ and a point ? ∞ so as to obtain a compact space, the ‘extended real line’ ?.; the student has made use of this for a long
5#
發(fā)表于 2025-3-22 08:52:20 | 只看該作者
Limits of Functions, tend simply, to a function .. In this chapter we study these concepts in the general setting of metric spaces. We obtain in this way certain of the ‘infinite-dimensional’ spaces alluded to in the Introduction, and, thanks to Ascoli’s theorem, the . of these spaces.
6#
發(fā)表于 2025-3-22 15:56:43 | 只看該作者
Normed Spaces,ms. In §§6, 7, 8 we make the connection between this theory and that of complete spaces; some of these results (Banach-Steinhaus theorem, Riesz’s theorem) are very fruitful, but the reader can hardly be convinced of this unless (s)he studies ‘functional analysis’ later on.
7#
發(fā)表于 2025-3-22 17:12:03 | 只看該作者
Connected Spaces,istinguish, by various methods, those spaces that are ‘in one piece’ (for example a disc, or the complement of a disc in a plane) and those which are not (for example, the complement of a circle in a plane).
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發(fā)表于 2025-3-22 22:59:14 | 只看該作者
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https://doi.org/10.1007/978-981-16-7723-6 tend simply, to a function .. In this chapter we study these concepts in the general setting of metric spaces. We obtain in this way certain of the ‘infinite-dimensional’ spaces alluded to in the Introduction, and, thanks to Ascoli’s theorem, the . of these spaces.
10#
發(fā)表于 2025-3-23 08:54:11 | 只看該作者
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