In a relative covering dimension is defined and studied which is denoted by r-dim. In this paper we give an algorithm of polynomial order for computing the dimension r-dim of a pair (Q,X), where Q is a subset of a finite space X, using matrix algebra.

Abstract In every finite poset (X, ≤) we assign the so called order-matrix , where αij ∈ {−2, 0, 1, 2}. Using this matrix, we characterize the order dimension of an arbitrary finite poset.

Using this characterization of small inductive dimension ind, an algorithm for computing the dimension ind is presented and an upper bound on the number of iterations of the algorithm is computed.Expand

Two selection games from the literature, Gc(O,O) and G1(Ozd,O), are known to characterize countable dimension among certain spaces. This paper studies their perfectand limitedinformation strategies,… Expand

In [7] (see also [2, p. 35]) two relative covering dimensions, denoted by dim and
dim
, defined and studied. In [3] and [4] we studied these dimensions and we gave some properties
including… Expand

The articles [15], [8], [2], [5], [16], [6], [14], [19], [10], [12], [17], [9], [11], [3], [4], [13], [7], [18], and [1] provide the notation and terminology for this paper. The scheme Set of… Expand