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Tuesday , August 22 2017
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Functional Analysis

Suppose K and C are subsets of a topological vector space X, K is compact, C is closed, and K n C = ∅. Then 0 has a neighborhood of V such that (K + V) n (C + V) = ∅.

Proof: If  K = ∅, then K + V = ∅, and the conclusion of the theorem is obvious. We therefore assume that K # ∅, and consider a point x ∈ K. Then x ∉ C ⟹ x ∈ CC. Since C is closed, ∃ a neighborhood W of ...

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