𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On (ℝ(L), ⊕)

✍ Scribed by R. Lowen

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
305 KB
Volume
10
Category
Article
ISSN
0165-0114

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✦ Synopsis

We prove there exists a somewhat simpler description of R(L) and its fuzzy topology than the one given by Hutton

[2] and a considerably simpler description of @ than the one given by Rodahaugh [4]. As a result of this simplification we are able to give a direct proof of the continuity of $, an open problem in 141.

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## Abstract Let {__I__~__k__~}~__k__∈ℕ~ be a sequence of well–distributed mutually disjoint intervals of ℝ\{0}. For __f__ ∈ __L__^__p__^(ℝ), 1 ≤ __p__ ≤ 2, define __S____f__ by (__S____f__)ˆ = χ$\hat f $. We prove that there exists a positive constant __C__ such that for all __f__ ∈ __L__^__p__^(ℝ