Modern Topology

Non-Hausdorff Topology and Domain Theory: Selected Topics in Point-Set Topology (New Mathematical Monographs, Book 22)

Non-Hausdorff Topology and Domain Theory: Selected Topics in Point-Set Topology (New Mathematical Monographs, Book 22) by Jean Goubault-Larrecq
English | 2013 | ISBN: 1107034132 | ISBN-13: 9781107034136 | 497 pages | PDF | 3,1 MB

This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff.
Introduction to Topology and Modern Analysis (Repost)

George F. Simmons, "Introduction to Topology and Modern Analysis"
English | 1963 | ISBN: 1575242389, ASIN: B007BNGNRI | DJVU | pages: 390 | 9,1 mb
Orbifolds and Stringy Topology (Cambridge Tracts in Mathematics) [Repost]

Orbifolds and Stringy Topology (Cambridge Tracts in Mathematics) by Johann Leida
English | June 25, 2007 | ISBN: 0521870046 | 164 Pages | PDF | 4.83 MB

An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry.

Modern Analysis and Topology [Repost]  

Posted by ChrisRedfield at July 28, 2015
Modern Analysis and Topology [Repost]

Norman R. Howes - Modern Analysis and Topology
Published: 1995-06-23 | ISBN: 0387979867 | PDF + DJVU | 444 pages | 34.76 MB

Elementary Topology and Applications by Carlos R. Borges  

Posted by tanas.olesya at March 26, 2015
Elementary Topology and Applications by Carlos R. Borges

Elementary Topology and Applications by Carlos R. Borges
English | Jan 15, 2001 | ISBN: 9810242409 | 215 Pages | PDF | 6 MB

The material in this book is organized in such a way that the reader gets to significant applications quickly, and the emphasis is on the geometric understanding and use of new concepts. The theme of the book is that topology is really the language of modern mathematics.

A Concise Course in Algebraic Topology  

Posted by interes at Oct. 24, 2014
A Concise Course in Algebraic Topology

A Concise Course in Algebraic Topology by J. P. May
English | 1999 | ISBN: 0226511839 | 254 pages | PDF | 1,6 MB

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups.
Modern Geometry - Methods and Applications: Part II: The Geometry and Topology of Manifolds

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov - Modern Geometry - Methods and Applications: Part II: The Geometry and Topology of Manifolds
Published: 1985-09-01 | ISBN: 3540961623, 0387961623 | PDF + DJVU | 432 pages | 11 MB

Undergraduate Topology: A Working Textbook  

Posted by interes at July 24, 2014
Undergraduate Topology: A Working Textbook

Undergraduate Topology: A Working Textbook by Aisling McCluskey and Brian McMaster
English | 2014 | ISBN: 0198702337 , 0198702345 | 160 pages | PDF | 1 MB

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves.
Fibrewise Topology (Cambridge Tracts in Mathematics, Book 91)

Fibrewise Topology (Cambridge Tracts in Mathematics, Book 91) by I. M. James
English | 1989 | ISBN: 0521360900 | ISBN-13: 9780521360906 | 208 pages | PDF | 8,7 MB

The aim of this book is to promote a fibrewise perspective, particularly in topology, which is central to modern mathematics. Already this view is standard in the theory of fibre bundles and therefore in such subjects as global analysis. It has a role to play also in general and equivariant topology.
The General Topology of Dynamical Systems (Graduate Studies in the Mathematical Sciences, V. 1)

The General Topology of Dynamical Systems (Graduate Studies in the Mathematical Sciences, V. 1) by Ethan Akin
English | 1993 | ISBN: 0821838008 | ISBN-13: 9780821838006 | 261 pages | DJVU | 2,7 MB

Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets).