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Let (X, B, µ, T ) be a dynamical system and (Y, A, ν, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, ν, S). We define relative sequence entropy pairs and using them, we find the relative topological µ-Kronecker factor over (Y, ν) which is the maximal topological factor having relative discrete spectrum over (Y, ν). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrumdoi:10.4134/jkms.2005.42.4.857 fatcat:itcegrni3zeutfzk4qixvprg2u