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A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable

C. R. Guilbault (2001)

Fundamenta Mathematicae

We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 𝒵-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.

A note on characteristic classes

Jianwei Zhou (2006)

Czechoslovak Mathematical Journal

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

A note on generalized flag structures

Tomasz Rybicki (1998)

Annales Polonici Mathematici

Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.

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