Topology, K. Janich

This book contains the edited version of lectures and contributed papers presented at the NA TO ADV ANCED RESEARCH WORKSHOP ON TOPOLOGY OPTIMIZATION OF STRUCTURES, held at Hotel do Mar, Sesimbra, Portugal, 20 June to 26 June, 1992, and organised by the Mathematical Institutc, The Technical University of Denmark and bv CEMUL-Center of Mechanics and Materials of the Techmcal University of Lisbon, Fifty participants from' fourteen countries attended the workshop,

The essentials of point-set topology, complete with motivation and numerous examples
Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.

Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

The first five chapters of this book form an introductory course in piece­ wise-linear topology in which no assumptions are made other than basic topological notions. This course would be suitable as a second course in topology with a geometric flavour, to follow a first course in point-set topology, andi)erhaps to be given as a final year undergraduate course. The whole book gives an account of handle theory in a piecewise­ linear setting and could be the basis of a first year postgraduate lecture or reading course. Some results from algebraic topology are needed for handle theory and these are collected in an appendix. In a second appen­ dix are listed the properties of Whitehead torsion which are used in the s-cobordism theorem. These appendices should enable a reader with only basic knowledge to complete the book. The book is also intended to form an introduction to modern geo­ metric topology as a research subject, a bibliography of research papers being included. We have omitted acknowledgements and references from the main text and have collected these in a set of "historical notes" to be found after the appendices.