## Topics in functional analysis |

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balanced neighborhood Banach space barreled BH space borhood bornivore bornological bounded set Cauchy sequence Chapter Choose closed graph closed neighborhoods closed set closure complete metric continuously embedded converges weakly convex linear topological coregular Corollary countable define Definition direct sum topology embedded in H eventually Example 1.1 f is_ finite dimensional Frechet space ft(r Hausdorff space Hausdorff topology hence implies inclusion map inductive limit integer Lemma Let f e Let f:X Let H Let Jx linear map linear space linear subspace linear topological space locally convex linear locally convex spaces locally convex topology N-sequential norm bounded norm space normalized infimum open neighborhood Proof Remark Seiten semi-bornological sequence of BH sequential neighborhood sequentially closed sequentially continuous space is called Sufficiency supremum test topology Theorem 2.1 trivial unrestricted inductive limit W-barreled weak