Description

The main goal of the book is to give a concise, in-depth overview of fundamental concepts in the study of collections of items, or set, that have a mathematical structure. This book's goal was to provide a comprehensible introduction to algebraic topology with a wide range of material covered. The perspective is extremely traditional in nature and adheres closely to the boundaries of pure algebraic topology. The study of topology emerged from geometry and set theory through the examination of ideas like space, dimension, and transformation. Such concepts date back to Gottfried Leibniz, who proposed the geometria situs and analysis situs in the 17th century. Perhaps the first theorems in the discipline were Leonhard Euler's solutions to the Seven Bridges of Kˆnigsberg Problem and Polyhedron Formula. Johann Benedict Listing coined the term "topology" in the 19th century, but the concept of a topological space wasn't defined until the early 20th century. The study of topology had grown to be a significant area of mathematics by the middle of the 20th century. The driving idea behind topology is that certain geometric issues are determined less by the precise geometry of the objects involved and more by their arrangement.