More figuratively, you can see that several trees near the teaching building are an undirected graph. The bifurcation point of leaves and branches is the node of the graph, and branches are the edges of the graph. Every tree is connected, but there are no branches between trees. So every tree can be regarded as a connected branch, and the number of trees is the number of connected branches.
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.
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Topological space X is a connected space if and only if X is its only connected branch. 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, and X is a multipoint topological space. If every single point set of topological space X is a connected branch of X ..
The largest connected subset of a topological space is called a connected unit, and each space can be represented as a disjoint cross-linked set of its connected units. Connected units must be closed and open in sufficiently good spaces (such as manifolds and algebraic clusters), but this is not always the case.
For example, the connected units on a rational number set are all single element sets. If the connected units of a space are all single element sets, it is called a totally disconnected space. Many topological spaces constructed in algebraic number theory belong to this category.
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