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1

Strongly monotypic polytopes in R3

Borowska D., Grzybowski J.

Demonstratio Mathematica

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2008

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Vol. 41, nr 1

165-169

EN

McMullen et al. [3] characterized all three-dimensional monotypic polytopes by presenting four types of such polytopes. They stated that three of these types are strongly monotypic polytopes. We examine which monotypic polytopes of the fourth type are strongly monotypic. This way we complete the description of all strongly monotypic polytopes in R3.

2

Compacta not embeddable into Cartesian products of curves

Dydak J., Koyama A.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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Vol. 48, no 1

51-56

EN

We prove that an n-dimensional compactum X cannot be embedded into the Cartesian product of n curves if there is a group G such that [H^1] (X;G) = 0 and [H^n](X;G) [is not equal to] O.

3

Borsuk-Ulam type theorems on product spaces. 1

Dzedzej Z., Idzik A., Izydorek M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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Vol. 48, no 4

379-386

EN

The ideal-valued G-index theory is used to prove Borsuk-Ulam and Bourgin-Yang type theorems on the product of spheres. A generalization of a theorem of Zhong is given.

4

Point glueing in cpo-s

Sokołowski S.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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1998

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nr 863

3-22

EN

This report explains how to factor partial orders to get quotient partial orders and how to factor cpo-s to get quotient cpo-s. This is supplemented by an important issue of collapsing the cpo-s to simpler ones. The motivations for this research come from investigations of concurrent processes addressed elsewhere. However, the article may be read independently of these motivations.

PL

W tej pracy wyjasniam jak dzielić porządki częściowe przez relacje równoważności, żeby otrzymać porządki częściowe oraz jak dzielić zupełne łańcuchowo porządki częściowe (cpo-ty) przez relacje równoważności, żeby otrzymać cpo-ty. Dalej omawiam ważne zagadnienie kolapsowania cpo-tów do prostszej postaci. Motywacje pochodzą z omawianych gdzie indziej badań procesów współbieżnych. Jednak niniejszy artykuł można czytać niezależnie od tych motywacji.

5

On T-modifications of mappings into surfaces

Karno Z.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 4

345-350

EN

It is shown that if X is a compact 2-dimensional polyhedron and if f is a mapping of X to a surface M, then f x id[sub Ik] (f x id[sub Sk], respectively) is essential for every [k is greater than or equal to 0] if and only if each T-modification of f is essential.

6

On the shape asphericity of compacta

Yokoi K.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 3

249-264

EN

Dydak and the autor [1] introduced the notion of shape aspherical compacta: a compactum X is shape aspherical if any map f : X --> P from X to a polyhedron P factors up to homotopy as f[...] hog, where g : X --> K, h : K --> P and K is an aspherical CW-complex (i.e., K is a K (G,1)), and modified some results known to be true for the class of strongly hereditarily aspherical compacta, which is introduced by Daverman [2]. In this paper, we shall investigate fundamental properties of the (shape) asphericity.