Title: Semicontinuity of rank and nullity and some consequences
Abstract: One can easily verify that f is continuous if and only if it is both upper and lower semicontinuous. One might gain some insight into semicontinuity by showing that a set A ⊂ X is open (resp. closed) if and only if the characteristic function χA is lower (resp. upper) semicontinuous. We shall refrain here from a detailed discussion of semicontinuity, although such a discussion is worth having. We refer the reader to [Willard 1970].
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: article
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Cited By Count: 5
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