Математички Билтен ISSN 0351-336X (print) Vol. 40(LXVI) No. 3 ISSN 1857-9914 (online) 2016 (43-49) UDC: 515.124.3 Скопје, Македонија ON (3,2,)-S-K-METRIZABLE SPACES Sonja Čalamani 1 , Dončo Dimovski 2 Marzanna Seweryn-Kuzmanovska 3 Abstract. For a given (3, 2, )  - metric d on a set M, we show that any (3, 2, )  -S-K-metrizable space has an open refinement which is both locally finite and -discrete 1. INTRODUCTION If we review historically the geometric properties, their axiomatic classification and the generalization of metric spaces we can see that, they have been subject of interest of great number of mathematicians and from their work a lot of have been developed. We will mention some of them: K. Menger ([14]), V. Nemytzki, P. S. Aleksandrov ([16], [1]), Z. Mamuzic ([13]), S. Gähler ([11]), A. V. Arhangelskii, M. Choban, S. Nedev ([2], [3], [17]), R. Kopperman ([12]), J. Usan ([18]), B. C. Dhage, Z. Mustafa, B. Sims ([6], [15]). The notion of (, , ) nm  - metric is introduced in [7]. Connections between some of the topologies induced by a (3,1, )  -metric  and topologies induced by a pseudo-o-metric, o-metric and symmetric are given in [8]. For a given (3, , ) j  -metric d on a set M , {1, 2}, j  seven topologies ( , ), ( , ), ( , ), ( , ), ( , ), ( , ) Gd Hd Dd Nd Wd Sd       and ( , ) Kd  on , M induced by , d are defined in [4], and several properties of these topologies are shown. In this paper we consider only the topologies (, ) Sd  and ( , ) Kd  induced by a (3, 2, )  -metric d and for (, ) ( , ) Sd Kd      we prove that any open cover of a (3, 2, )  -S-K-metrizable space ( ,) M  has: a) an open refinement which is both locally finite and  -discrete, b)  -discrete base, and c) a (3, 2, )  -S-K-metri- _______________________________________ 2010 Mathematics Subject Classification. 54A10, 54E35, 54E99 Key words and phrases. (3, 2, )  -metric, (3, 2, )  -S-K-metrizable spaces