Question

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

Answer 1

$\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_2$