Examples of functions -extendable for each finite, but not ∞ -extendable

Wiesław Pawłucki

Banach Center Publications (1998)

  • Volume: 44, Issue: 1, page 183-187
  • ISSN: 0137-6934

Abstract

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In Example 1, we describe a subset X of the plane and a function on X which has a k -extension to the whole ℝ 2 for each finite, but has no ∞ -extension to ℝ 2 . In Example 2, we construct a similar example of a subanalytic subset of ℝ 5 ; much more sophisticated than the first one. The dimensions given here are smallest possible.

How to cite

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Pawłucki, Wiesław. "Examples of functions $^$-extendable for each finite, but not $^∞$-extendable." Banach Center Publications 44.1 (1998): 183-187. <http://eudml.org/doc/208881>.

@article{Pawłucki1998,
abstract = {In Example 1, we describe a subset X of the plane and a function on X which has a $^k$-extension to the whole $ℝ^2$ for each finite, but has no $^∞$-extension to $ℝ^2$. In Example 2, we construct a similar example of a subanalytic subset of $ℝ^5$; much more sophisticated than the first one. The dimensions given here are smallest possible.},
author = {Pawłucki, Wiesław},
journal = {Banach Center Publications},
keywords = {extension of -functions; subanalytic sets; algebras of germs of analytic functions},
language = {eng},
number = {1},
pages = {183-187},
title = {Examples of functions $^$-extendable for each finite, but not $^∞$-extendable},
url = {http://eudml.org/doc/208881},
volume = {44},
year = {1998},
}

TY - JOUR
AU - Pawłucki, Wiesław
TI - Examples of functions $^$-extendable for each finite, but not $^∞$-extendable
JO - Banach Center Publications
PY - 1998
VL - 44
IS - 1
SP - 183
EP - 187
AB - In Example 1, we describe a subset X of the plane and a function on X which has a $^k$-extension to the whole $ℝ^2$ for each finite, but has no $^∞$-extension to $ℝ^2$. In Example 2, we construct a similar example of a subanalytic subset of $ℝ^5$; much more sophisticated than the first one. The dimensions given here are smallest possible.
LA - eng
KW - extension of -functions; subanalytic sets; algebras of germs of analytic functions
UR - http://eudml.org/doc/208881
ER -

References

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  8. [8] B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, Bombay, 1966. 
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