In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0's and 1's which is
not A-summable. In 1943, R. C. Buck characterized convergent
sequences as follows: a sequence x is convergent if and only if
there exists a regular matrix A which sums every subsequence of
x. In this paper, definitions for subsequences of a double
sequence and Pringsheim limit points of a double sequence are
introduced. In addition, multidimensional analogues of Steinhaus'
and Buck's theorems are proved.