Detailed Topology Guide
Introduction to Topology
Topology is a branch of mathematics that studies the properties of geometric shapes that do not change when they are continuously transformed. It has wide applications in various fields such as computer networks, physics, economics, etc. In this tutorial, we will cover the basic concepts and terms related to topology.
Basic Terms
The following basic terms are used in topology:
Topological space: is a set of points endowed with a topological structure that allows us to determine which subsets are open and which are closed.
Open set: is a set of points each of which has a neighborhood contained in this set.
Closed set: is a set whose complement is an open set.
Continuous map: is a map between two topological spaces that preserves the topological structure.
Examples of Topological Spaces
There are many examples of topological spaces, some of which we will consider below:
Euclidean space: is the space we know from school geometry. It is an example of a metric space.
Torus: is the space obtained by gluing the opposite sides of a square. It is an example of a compact space.
Sphere: is the space obtained by gluing all the points on the surface of a ball into a single point. It is an example of a connected and compact space.
For a more in-depth study of topology, it is recommended to read additional literature and examples. It is also worth mentioning that there are different approaches to topology, such as algebraic topology, differential topology, and set theory, each with its own characteristics and applications.
Topology is an interesting and important area of mathematics that can help understand many phenomena in fields ranging from physics to economics to computer science. Studying topology can be challenging, but visual examples and practical applications can help you better understand the field.
This book is a guide to learning the basics of SubD (subdivision surface) topology. It features over sixty exercises filled with a variety of tips, tricks, and techniques designed to teach you how to manipulate polygon mesh topology.
Throughout the book, you will also find many images of polygon mesh topologies of objects that you can study for reference.
This book does not show you how to build a car, character, or creature. Instead, it teaches the basics of working with SubD topology, so you can create any SubD object with clean polygon flow.
Enjoy your study🔽
Publisher: Gumroad
Year: 2018
Pages: 128