A study of a covering dimension of finite lattices

摘要

Indubitably, the notion of covering dimension of frames was, extensively, studied. Many searches such as Charalambous, Banashewski and Gilmour (see, for example (Charalambous, 1974; Charalambous, 1974 [11]; Banaschewski and Gilmour, 1989 [12]) studied this dimension. Also, in the study [5], the covering dimension of finite lattices has been characterized by using the so called minimal covers. This approach gave the motive to other searches such as Zhang et al., to study properties of this dimension (see Zhang et al. (2017) [9]). In this paper, we study the covering dimension of finite lattices in combination with matrix theory. Essentially, we characterize the minimal covers of finite lattices and the order of those covers using matrices and we compute the covering dimension of the corresponding finite lattices.