Inductive dimensions modulo simplicial complexes and $ANR$-compacta

V. V. Fedorchuk¹

¹ Faculty of Mechanics and Mathematics Moscow State University Moscow 119992, Russia

Colloquium Mathematicum, Tome 120 (2010) no. 2, pp. 223-247

Résumé

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 $K\hbox{-}{\rm dim}\, X$.

Détail

DOI : 10.4064/cm120-2-4

Keywords: introduce investigate inductive dimensions cal hbox mathop ind cal hbox mathop ind classes cal finite simplicial complexes classes cal anr compacta cal consists sphere only cal hbox mathop ind dimension identical classical large inductive dimension ind compare hbox mathop ind hbox mathop ind introduced author mat vesnik particular every complex ast non contractible construct compact hausdorff space hbox mathop ind equal hbox dim