On finitistic spaces

Finitistic spaces form a natural class containing compact and finite-dimensional spaces. Introduced and investigated by fixed-point theorists, finitistic spaces found an application in cohomological dimension theory. In the paper, two characterizations of paracompact, finitistic spaces are proved. These characterizations allow to create a mechanism of generalizing results of finite dimension theory. As an application we obtain results on compact group actions on paracompact spaces which were previously known for compact Lie group actions.