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Errata to the paper "Families of convex sets closed under intersection, homotheties and uniting increasing sequences of sets" Fundamenta Mathematicae 120 (1984), pp. 14-40

100%

Lassak M.

Fundamenta Mathematicae

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1984

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tom 124

|

nr 3

287

2

Reduced spherical polygons

100%

Lassak M.

Colloquium Mathematicum

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2015

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tom 138

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nr 2

205-216

EN

For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere $S^{d}$ we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body $R ⊂ S^{d}$ is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We also estimate the diameter of reduced spherical polygons in terms of their thickness. Moreover, a few other properties of reduced spherical polygons are given.

3

A measure of axial symmetry of centrally symmetric convex bodies

64%

Lassak M., Nowicka M.

Colloquium Mathematicum

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2010

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tom 121

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nr 2

295-306

EN

Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for axs(P) for every parallelogram P.

4

Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets

63%

Lassak M.

Fundamenta Mathematicae

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1984

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tom 120

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nr 1

15-40

5

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Terminal subsets of convex sets in finite-dimensional real normed spaces

51%

Lassak M.

Colloquium Mathematicum

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1985-1986

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tom 50

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nr 2

249-255

6

Carathéodory's and Helly's dimensions of products of convexity structures

51%

Lassak M.

Colloquium Mathematicum

|

1982

|

tom 46

|

nr 2

215-225

7

Superior estimation of Carathéodory's dimension for n-cell convexity

44%

Lassak M.

Colloquium Mathematicum

|

1982

|

tom 46

|

nr 2

227-232

8

О независимости точек метрического пространства

32%

Lassak M.

Fundamenta Mathematicae

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1977

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tom 96

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nr 1

53-66

9

Convex half-spaces

26%

Lassak M.

Fundamenta Mathematicae

|

1984

|

tom 120

|

nr 1

7-13

Ograniczanie wyników

5 Colloquium Mathematicum

4 Fundamenta Mathematicae

9 Lassak M.

1 Nowicka M.

1 2015

1 2010

1 1986

3 1984

2 1982

1 1977

Errata to the paper "Families of convex sets closed under intersection, homotheties and uniting increasing sequences of sets" Fundamenta Mathematicae 120 (1984), pp. 14-40

Reduced spherical polygons

A measure of axial symmetry of centrally symmetric convex bodies

Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets

Terminal subsets of convex sets in finite-dimensional real normed spaces

Carathéodory's and Helly's dimensions of products of convexity structures

Superior estimation of Carathéodory's dimension for n-cell convexity

О независимости точек метрического пространства

Convex half-spaces