Inductive dimensions modulo P
by
Vitalij A. Chatyrko
Linköping University, Sweden
Coauthors: Y. Hattori

All spaces are assumed to be separable and metrizable. Recently, we defined the spaces S^a_Y, where a is any countable ordinal number and Y is any space, by the use of construction of the Smirnov's compacta S^a. (In particular, if Y is a one-point space then S^a_Y is the compactum S^a). Then we applied the generalized Smirnov's spaces S^a_Y, where a's are countable ordinals and Y's are special zero-dimensional subspaces of the closed interval [0, 1], for a complete description of the relationship between all transfinite dimensions modulo P, P-trInd, where P is any absolutely multiplicative or additive Borel class, on separable metrizable spaces. Now we extend some known results about the relationship between the transfinite dimensions trind and trInd on the Smirnov's compacta S^a to the relationship between the transfinite dimensions modulo P, P-trind and P-trInd, where P is an absolutely multiplicative or additive Borel class, on the spaces S^a_Y, where Y is any finite-dimensional space.

Date received: April 30, 2008