Dimensions -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 Δ m − 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.