Around the equality indX=IndX towards to a unifying theorem

We give two positive results related to Ivanovʹs question [Vestnik Moskov. Univ. Ser. I Mat. Meh. 31 (4) (1976) 21–27, Question 1] concerning the sum theorem for dimension Ind0 introduced by Filippov. Using the results we generalize Fedorchukʹs theorem [Dokl. Akad. Nauk SSSR 234 (1) (1977) 30–33, Proposition 2] about the coincidence of small and large inductive dimensions ind and Ind in the class of completely paracompact hereditarily perfectly κ-normal spaces. We also prove a unifying theorem covering the generalization theorem and the results about the coincidence of ind and Ind from [V.A. Chatyrko, Y. Hattori, Bull. Polish Acad. Sci. 50 (2002) 255–265].