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ExamplesCounterexamples: Let $V=\mathbb R$ and let $E$ be the base for the usual topology consisting of the open intervals, or the subbase consisting of the open rays of the form $(a,\infty)$ and $(-\infty,a)$.
Examples: Let $V=\mathbb R$ and let $E$ be the base for the usual topology consisting of the open intervals, or the subbase consisting of the open rays of the form $(a,\infty)$ and $(-\infty,a)$.
Counterexamples: Let $V=\mathbb R$ and let $E$ be the base for the usual topology consisting of the open intervals, or the subbase consisting of the open rays of the form $(a,\infty)$ and $(-\infty,a)$.
Examples: Let $V=\mathbb R$ and let $E$ be the base for the usual topology consisting of the open intervals, or the subbase consisting of the open rays of the form $(a,\infty)$ and $(-\infty,a)$.
