Transfinite extension of dimension function

In this article we define the transfinite dimension function tr - ( m , n ) - dim . The main results are the following:(1) be a space and let X 1 and X 2 be closed subsets of X such that X = X 1 ∪ X 2 . r - ( m , n ) - dim X ⩽ max ( tr - ( m , n ) - dim X 1 , tr - ( m , n ) - dim X 2 ) ⊕ ( tr - ( m , n ) - dim ( X 1 ∩ X 2 ) + 1 ) . ery space X tr - ( m , n ) - dim X ⩽ tr - ( m , n ) - Ind X .