Fundamentals of Topology

About The Book

The primary goal of this book is to present a straightforward, complete treatment of fundamental themes in the study of collections of objects, or sets, that have a mathematical structure. This book was meant to provide a readable introduction to algebraic topology that covers a wide range of topics. The point of view is extremely classical in spirit, and it keeps within the bounds of pure algebraic topology. Topology arose as a branch of study from geometry and set theory, analysing concepts such as space, dimension, and transformation. Such concepts can be traced back to Gottfried Leibniz, who proposed the geometria situs and analysis situs in the 17th century. The Seven Bridges of Konigsberg Problem and the Polyhedron Formula by Leonhard Euler are often regarded as the field's initial theorems. Johann Benedict Listing coined the term topology in the nineteenth century, but the concept of a topological space did not emerge until the first decades of the twentieth century. By the mid-twentieth century, topology had established itself as a major subject of mathematics. The motivating notion behind topology is that some geometric issues are determined not by the actual shape of the objects involved, but by how they are assembled. The square and the circle, for example, share many properties: they are both one-dimensional objects (from a topological standpoint) and both divide the plane into two sections, the inside and the outside.