# What does it mean for a topological space $X$ to have a binary open cover?

Does someone know what's meant by a binary open cover of a topological space $X$? I can't find this definition of binary open cover. Could someone who knows it tell me? Thanks ahead for any help:)

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It might mean "open cover consisting of two open sets". What's the context? – Zhen Lin Jun 26 '12 at 9:36
Maybe you should give the context. If the definition is non-standard it is hard to guess. The word binary suggests that the cover consists of precisely two open sets. – Simon Markett Jun 26 '12 at 9:36

## 1 Answer

A binary open cover of a space $X$ is simply an open cover with exactly two members. For example, a $T_1$ space is normal iff every binary (= two-element) open cover of $X$ has a binary closed refinement. (This is an easy exercise.)

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