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Math Help - Local base

  1. #1
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    Local base

    Let B be a local base for a topological vector space X. Let U be a neighborhood of 0 in X. Show that \cap_{W \in B} (U \cap W) = \cap_{W \in B} W.
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  2. #2
    tah
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    Obviously, \cap_{W\in B}(U\cap W)\subseteq\cap_{W\in B}W.
    Let  x\in \cap_{W\in B}W and O\in B such that O\subseteq U (definition) then x\in O\subseteq U i.e. x\in U\cap W for any W\in B
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