It means that a graph is divided into several small blocks, and each small block is connected, but the small blocks are not connected, so each small block is called a connected branch, and the isolated point is also a connected branch.

Let x be a topological space, and if c satisfies:

(1)C is a connected subset of topological space x;

(2) If C is not a proper subset of any connected subset of topological space X, then C is called a connected branch (or maximal connected subset) of topological space X..

Extended data:

All connected branches of topological space X are a classification of X, in other words, every connected branch of X is a nonempty set; Different connected branches of x do not intersect; The sum of all connected branches of x is X.

A discrete space with more than one point is completely disconnected. Topological space X is a connected space if and only if X is its only connected branch.

Topological space as an object and continuous mapping as a morphism constitute the category of topological space, which is a basic category in mathematics. The idea of trying to classify this category through invariants inspired and produced the research work in the whole field, including homoethics theory, homology theory and K- theory.

Quotient topology can be defined as follows: if x is a topological space, y is a set, and if f:X→Y is a surjection, y obtains a topology; The open set of topology can be defined as follows: a set is open if and only if its inverse image is also open.

The equivalence class on lower X can be determined by F natural projection, thus an equivalence relation on topological space X is given.

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