Differential Topology pp 1-6 | Cite as

# Introduction

Chapter

## Abstract

In many branches of mathematics one finds spaces that can be described locally by *n*-tuples of real numbers. Such objects are called manifolds: *a manifold is a topological space which is locally homeomorphic to Euclidean n-space* ℝ^{ n }. We can think of a manifold as being made of pieces of ℝ^{n} glued together by homeomorphisms. If these homeomorphisms are chosen to be differentiable, we obtain a *differentiable manifold*. This book is concerned mainly with differentiable manifolds.

## Keywords

Vector Bundle Riemann Surface General Position Homotopy Class Algebraic Topology
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## Copyright information

© Springer-Verlag New York Inc. 1976