Wyniki wyszukiwania

1

Smooth approximations without critical points

100%

Hájek P., Johanis M.

Open Mathematics

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2003

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tom 1

|

nr 3

284-291

EN

In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set residual in some neighbourhood of zero.

2

Analytic and $C^k$ approximations of norms in separable Banach spaces

81%

Deville R., Fonf V., Hájek P.

Studia Mathematica

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1996

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tom 120

|

nr 1

61-74

EN

We prove that in separable Hilbert spaces, in $ℓ_{p}(ℕ)$ for p an even integer, and in $L_{p}[0,1]$ for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In $ℓ_{p}(ℕ)$ and in $L_{p}[0,1]$ for p ∉ ℕ (resp. for p an odd integer), every equivalent norm can be approximated uniformly on bounded sets by $C^[p]}$-smooth norms (resp. by $C^{p-1}$-smooth norms).

3

Diameter 2 properties and convexity

71%

Abrahamsen T., Hájek P., Nygaard O., Talponen J., Troyanski S.

Studia Mathematica

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2016

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tom 232

|

nr 3

227-242

EN

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of C[0,1] with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.

4

On interpretability in theories containing arithmetic

70%

Hájková M., Hájek P.

Fundamenta Mathematicae

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1972

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tom 76

|

nr 2

131-137

5

Degrees of dependence in the theory of semisets.

60%

Hájek P.

Fundamenta Mathematicae

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1974-1975

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tom 82

|

nr 1

11-24

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Studia Mathematica

1 Open Mathematics

5 Hájek P.

1 Abrahamsen T.

1 Deville R.

1 Fonf V.

1 Hájková M.

1 Johanis M.

1 Nygaard O.

1 Talponen J.

1 Troyanski S.

1 2016

1 2003

1 1996

1 1974

1 1972

Smooth approximations without critical points

Analytic and $C^k$ approximations of norms in separable Banach spaces

Diameter 2 properties and convexity

On interpretability in theories containing arithmetic

Degrees of dependence in the theory of semisets.