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Abstract

We introduce and investigate inductive dimensions ${\cal K}\hbox{-}\mathop{\rm Ind} $ and ${\cal L}\hbox{-}\mathop{\rm Ind} $ for classes ${\cal K}$ of finite simplicial complexes and classes ${\cal L}$ of $ANR$-compacta (if ${\cal K}$ consists of the 0-sphere only, then the ${\cal K}\hbox{-}\mathop{\rm Ind} $ dimension is identical with the classical large inductive dimension Ind). We compare $K\hbox{-}\mathop{\rm Ind} $ to $K\hbox{-}\mathop{\rm Ind} $ introduced by the author [Mat. Vesnik 61 (2009)]. In particular, for every complex $K$ such that $K \ast K$ is non-contractible, we construct a compact Hausdorff space $X$ with $K\hbox{-}\mathop{\rm Ind} X$ not equal to $K\hbox{-}{\rm dim}\, X$.