On inductive dimension modulo a simplicial complex

For a given simplicial complex K, V.V. Fedorchuk has recently introduced the dimension functions K-dim and K-Ind and constructed a first countable and separable continuum Xn such that for each integer n>1, provided the join K⁎K is non-contractible. We study a modification K-Ind0 of K-Ind and develop its theory to a point that enables us to compute the inductive dimensions of a variety of spaces. Let α,β be ordinals of cardinality at most c and n an integer with 1⩽n⩽α⩽β. We construct, inter alia,(1)first countable and separable continua Sa with while ,(2)first countable and separable continua Sn,α with while ,(3)first countable, hereditarily strongly paracompact continua Tα such that while K-Ind0Tα=α,(4)first countable continua Tn,α,β with while , and K-Ind0Tn,α,β=β. For the construction of the spaces Sα and Tα it suffices to assume that K is non-contractible, while the construction of the spaces Sn,α and Tn,α,β for n>1 requires the stronger restriction that the join K⁎K is non-contractible.