@MISC{Wiid_sheafrepresentation, author = {F. G. J. Wiid}, title = {SHEAF REPRESENTATION OF NORMED SPACES}, year = {} }

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Abstract

Abstract. A multi-sorted lim-theory, which has as Set-valued models all normed spaces over some specified fields, is introduced. We show that co-herent extensions of this lim-theory are expressive enough to characterise, for example, the Lp-spaces. The sheaf-valued spectra, corresponding to the coherent extension of our lira-theory which chara•terises Hilbert spaces, are studied. Introduction. One of the advantages of studying a normed space X in the context of nonstandard analysis is that one has a supply of substitutes for X that behave like finite dimensional normcd spaces: if 5Y denotes the interpretation of X in a highly saturated model of set theory, then there exists a *-finite dimensional subspace Xf of 5Y such that Xf contains