Displaying 181 – 200 of 537

Showing per page

A note on linear mappings between function spaces

Jan Baars (1993)

Commentationes Mathematicae Universitatis Carolinae

Arhangel’skiǐ proved that if X and Y are completely regular spaces such that C p ( X ) and C p ( Y ) are linearly homeomorphic, then X is pseudocompact if and only if Y is pseudocompact. In addition he proved the same result for compactness, σ -compactness and realcompactness. In this paper we prove that if φ : C p ( X ) C p ( X ) is a continuous linear surjection, then Y is pseudocompact provided X is and if φ is a continuous linear injection, then X is pseudocompact provided Y is. We also give examples that both statements do not hold...

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

A note on the converse of the Lefschetz theorem for G-maps

M. Izydorek, A. Vidal (1993)

Annales Polonici Mathematici

The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.

Currently displaying 181 – 200 of 537