What Is Topology?

Topology is a discipline that studies some properties of geometric figures or spaces that can remain unchanged after continuous changes in shape. It only considers the positional relationship between objects without considering their shape and size.

Topology is a structure on a collection. Let T be a subset of the non-empty set X. If T meets the following conditions:

1.X and the empty set both belong to T;

2.The intersection of any two members of T belongs to T;

3. Any number of members in T belongs to T;

Then T is called a topology on X. A set X with a topology T is called a topology space and is denoted as (X, T).

Let T ₁ and T ₂ be the two topologies on the set X. If it matters T ₁

T ₂ , it is said that T _{1 is} thicker than T ₂ , or T _{2 is} thinner than T ₁ . When two topologies on X do not contain a relationship with each other, they are said to be incomparable. On set X,

Take 3DSMAX software as an example. When objects and shapes are created, a number is assigned to each vertex and / or face. Generally, these numbers are used internally to determine the vertices or faces selected at a given time. This numerical structure is called topology .

After selecting a vertex or face and applying a modifier to the selection, the modifier stack records the faces / vertices it affects. If you return to the stack selection level later, you can change the topology to apply the modifier.

The term topology refers to the structure and numbering of faces and vertices.

For example, by carefully setting various parameters, you can make the box and

In physics, topology is used in several fields, such as

The various possible positions of the robot can be described by a manifold called a configuration space. In the field of motion planning, the path between two points can be found in the configuration space. These paths represent the movement of the robot's joints and other parts into the desired position and posture. ^[6]