Page 1 Next

Displaying 1 – 20 of 123

Showing per page

A functional S-dual in a strong shape category

Friedrich Bauer (1997)

Fundamenta Mathematicae

In the S-category P (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual D X , X = ( X , n ) P , turns out to be of the same weak homotopy type as an appropriately defined functional dual ( S 0 ) X ¯ (Corollary 4.9). Sometimes the functional object X Y ¯ is of the same weak homotopy type as the “real” function space X Y (§5).

An approach to shape covering maps.

I. Pop (1999)

Revista Matemática Complutense

In this note we give an approach to shape covering maps which is comparable to that of *-fibrations (Mardesic and Rushing (1978)). The introduced notion conserves some important properties of usual covering maps.

Borsuk's quasi-equivalence is not transitive

Andrzej Kadlof, Nikola Koceić Bilan, Nikica Uglešić (2007)

Fundamenta Mathematicae

Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.

Currently displaying 1 – 20 of 123

Page 1 Next