THEORY OF I~*-FUNCTOR IN ALGEBRAIC TOPOLOGY I~*-FUNCTOR OF A FIBER SPACE

The present paper is a succession to the previous ones (e. g., [1]) concerning I~*-functor of a topological space. Its aim is twofold. First, we recast our theory about fiber square in a form under much more general conditions sufficient for all practical purposes. Secondly, we prove that the I~*-functor of a fiber space can be completely determined algebraically in terms of some twisted product of the I~*-functors of the base and the fiber, a theorem already announced under more stringent conditions in [2]. As this cannot be achieved for H~*-functor, our theorem shows once more the superiority of the I~*-funetor over the H~*-functor, so far as real coefficient domain is concerned.