What is "x" in this definition of a basis?

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Hill
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TL;DR
The definition in the book appears to be missing something.
In this definition,
1780180214205.webp

what is ##x## in the property (ii)?

Did they mean, "(ii) For any open ##V \subset X## and any ##x \in V##, there exists some ##U \in \mathscr{B}## with ##
x \in U## and ##U \subset V##?
Or something else?
 
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