Establish a.necessary and sufficient condition for a.family of subsets of a set X to be a.Q base for a topology on X
A family of subsets(Q) is said to be a base for a topology on x ifFor each x∈X, there exists B∈Q such that x∈BAlso if x∈B1∩B2 for some B1,B2∈Q, then there exists B∈Q such thatx∈B⊆B1∩B2\text{A family of subsets(Q) is said to be a base for a topology on x if}\\\text{For each $x \in X$, there exists $B \in Q$ such that $x \in B$}\\\text{Also if $x \in B_1 \cap B_2$ for some $B_1,B_2 \in Q$, then there exists $B \in Q$ such that}\\x\in B \subseteq B_1 \cap B_2A family of subsets(Q) is said to be a base for a topology on x ifFor each x∈X, there exists B∈Q such that x∈BAlso if x∈B1∩B2 for some B1,B2∈Q, then there exists B∈Q such thatx∈B⊆B1∩B2
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