Addition and product theorems for ind

In this paper we improve two theorems for the small inductive dimension ind in the regular T 1 -spaces: an addition theorem from [M.G. Charalambous, V.A. Chatyrko, Some estimates of the inductive dimensions of the union of two sets, Topology Appl. 146/147 (2005) 227–238] and a product theorem from [V.A. Chatyrko, K.L. Kozlov, On (transfinite) small inductive dimension of products, Comment. Math. Univ. Carolin. 41 (3) (2000) 597–603].