A Three-Space Property for Analytic Spaces
In this chapter, we show that analyticity is not a three-space property. We prove, however, that a metrizable tvs E is analytic if it contains a complete locally convex analytic subspace F such that the quotient E/F is analytic. We reprove (using Corson’s example) that the Lindelöf property is not a three-space property.
KeywordsBanach Space Closed Subspace Quotient Space Weak Topology Analytic Space
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