Dimensions (m,K)-dim and extensions of mappings

In Fedorchuk (2012) [1] dimensions (m,n)-dim were introduced. Here we define more general invariant (m,K)-dim (K is a simplicial subcomplex of (m−1)-dimensional simplex Δm−1) and prove that this dimension can be defined by means of extensions of mappings. We give also several equivalent definitions of dimensions (m,n)-dim.