# Examples of functions $$-extendable for each finite, but not ${}^{\infty}$-extendable

Banach Center Publications (1998)

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

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