國立高雄大學圖資館 |

Topology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topologyby Marco Manetti.
作者:	Manetti, Marco.
出版者:	Cham :Springer Nature Switzerland :2023.
面頁冊數:	xiv, 377 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Topology.
電子資源:	https://doi.org/10.1007/978-3-031-32142-9
ISBN:	9783031321429$q(electronic bk.)

Topology
Manetti, Marco.

Topology[electronic resource] /by Marco Manetti. - Second edition. - Cham :Springer Nature Switzerland :2023. - xiv, 377 p. :ill., digital ;24 cm. - La matematica per il 3+2,v. 1532038-5757 ;. - La matematica per il 3+2 ;v.113..

1 Geometrical introduction to topology -- 2 Sets -- 3 Topological structures -- 4 Connectedness and compactness -- 5 Topological quotients -- 6 Sequences -- 7 Manifolds, infinite products and paracompactness -- 8 More topics in general topology -- 9) Intermezzo -- 10 Homotopy -- 11 The fundamental group -- 12 Covering spaces -- 13 Monodromy -- 14 van Kampen's theorem -- 15 A topological view of sheaf cohomology -- 16 Selected topics in algebraic topology -- 17 Hints and solutions.

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications. It also corrects some inaccuracies and some additional exercises are proposed. The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

ISBN: 9783031321429$q(electronic bk.)

Standard No.: 10.1007/978-3-031-32142-9doiSubjects--Topical Terms:

185965
Topology.

LC Class. No.: QA611 / .M3613 2023

Dewey Class. No.: 514

Topology
LDR:02750nmm a2200361 a 4500 001 647883
003 DE-He213
005 20230901234246.0
006 m d
007 cr nn 008maaau
008 240116s2023 sz s 0 eng d
020 $a 9783031321429$q(electronic bk.)
020 $a 9783031321412$q(paper)
024 7 $a 10.1007/978-3-031-32142-9 $2 doi
035 $a 978-3-031-32142-9
040 $a GP $c GP
041 1 $a eng $h ita
050 4 $a QA611 $b .M3613 2023
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 514 $2 23
090 $a QA611 $b .M275 2023
100 1 $a Manetti, Marco. $3 276698
240 1 0 $a Topologia. $l English
245 1 0 $a Topology $h [electronic resource] / $c by Marco Manetti.
250 $a Second edition.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xiv, 377 p. : $b ill., digital ; $c 24 cm.
490 1 $a La matematica per il 3+2, $x 2038-5757 ; $v v. 153
505 0 $a 1 Geometrical introduction to topology -- 2 Sets -- 3 Topological structures -- 4 Connectedness and compactness -- 5 Topological quotients -- 6 Sequences -- 7 Manifolds, infinite products and paracompactness -- 8 More topics in general topology -- 9) Intermezzo -- 10 Homotopy -- 11 The fundamental group -- 12 Covering spaces -- 13 Monodromy -- 14 van Kampen's theorem -- 15 A topological view of sheaf cohomology -- 16 Selected topics in algebraic topology -- 17 Hints and solutions.
520 $a This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications. It also corrects some inaccuracies and some additional exercises are proposed. The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
650 0 $a Topology. $3 185965
650 0 $a Algebraic topology. $3 189702
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a La matematica per il 3+2 ; $v v.113. $3 825960
856 4 0 $u https://doi.org/10.1007/978-3-031-32142-9
950 $a Mathematics and Statistics (SpringerNature-11649)