A note on a sum theorem for dimension -Ind

Main results are:1. be a closed subspace of a hereditarily normal X such that K - Ind Y ⩽ n and K - Ind ( X ∖ Y ) ⩽ n . Then K - Ind X ⩽ n . be a perfectly normal space. Then a finite sum theorem for dimension K -Ind holds in X if and only if K -Ind is monotonic in X. ote by K a non-empty set of finite complete simplicial complexes.