Rational homotopy theory of shape one-connected spaces

Summary: "A rational shape type and a strong rational shape type are defined for the class of spaces 1-connected by shape. This class is a natural generalization of the class of 1-connected spaces for which the rational homotopic theory was constructed in work [10] [[msn] MR0258031 [/msn]]. With the use of the category of inverse systems, the result in [10] on the equivalence of homotopic theories is extended onto the class of spaces 1-connected by shape.