I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1998, VOLUME 4, NUMBER 1, PAGES 11-38
Ljusternik--Schnirelman theorem and
S. A. Bogatyi
View as HTML
View as gif image
View as LaTeX source
A generalization of the Aarts--Fokkink--Vermeer theorem ( and the space is
metrizable) is obtained.
free homeomorphisms of an -dimensional paracompact
space onto itself, the coloring number is not greater than .
As an application, it is obtained that for the free action of
a finite group on a normal (finite
dimensional paracompact) space , the coloring
and the genus of the space are related
As a corollary we prove that for all numbers and and the free action of
on the space the coloring
number is equal to in the theorem
It is shown that for any pairwise permutable free
continuous maps of an -dimensional compact
into itself, the coloring number does not exceed .
We generalise one theorem proved by Steinlein (about a free periodic
homeomorphism), who gave a negative solution to Lusternik's problem.
For any free map of a compact space into itself, the coloring number
does not exceed the Hopf number multiplied by four.
All articles are
published in Russian.
Last modified: April 8, 1998