topology Tau base Tau subset , so that any Open set All are Partial meta Union 。 [2-3] Set X as a set, Is a subset family of X. be Is the base of a topology on X, if and only if the following conditions are met (1) ； (2) If B one ,B two ∈ , and x ∈ B one ∩B two , B exists three ∈ , satisfying x ∈ B three ⊆B one ∩B two ； (2) 'If B one ,B two ∈ , then B one ∩B two Can be expressed as The union of a subset. Then there is a unique topology in X Is its base, called Generated Topology 。 [4] Let X be the topological space, Is an open set family of X. If for each subset U and each point x ∈ U in X, there exists B ∈ , so that x ∈ B ⊆ U, then Is the base of the topology on X. Let X be the topological space, Is a subset family of X. If for each point x ∈ U, there exists B ∈ Let x ∈ B ⊆ U, then U is an open set on X. [5] Correlation basis
Announce Let (X, τ) be topological space , τ 'is X Subset family 。 If τ is the intersection of all X topologies containing τ ', then τ' is said to be τ Subunit 。 [1] Equivalence is defined as
Let (X, τ) be a topological space and τ 'be a subset family of X. If all the finite intersection families of τ 'are the bases of τ, then τ' is said to be the subbase of τ. [4]
set up Is the open of x in topological space X Neighborhood Family. If any open neighborhood U of x contains at least one B ∈ , then by Neighborhood basis 。 [1] [3] Related concepts
Announce If the topology of topological space X has countable bases, then X is Second countable space 。 [3]
