Let L(I, J) be defined by the pull-back of CPT >#(Q, 2)< QSJ where {/, /} is a partition of all primes. We classify spaces (°° which have the same n-type for all n. In the category of finite CW-complexes, cancellation and non cancellation phenomena are well studied. In the category of infinite CW-complexes, the phenomena are less known. We study cancellation and non cancellation phenomena for infinite dimensional complexes by using above spaces.
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