IDefinition 1. (a) Let (X, G) be a quasi-ordered set. A subset E of X will be called increasing if x E E, y E X, x G y imply y E E (a decreasing set is defined dually). (b) An ordered space is a… (More)

are given which satisfy the following conditions: (1) VK,Y~L VCXQ ~a(Xny)=~U(x)n~,IY), (2) vx, YEL. VCWEJ, cp,(x u y) = cp,,(x) u iF,(yj7 (3’) va E J, i&(O) = 0, cp,( 1) = 1, (4) VXEL, Vad,… (More)

In [8, 11, 12] the class IRN was introduced in order to obtain the lattice-theoretic analogues of some results of Conrad (see e.g. [4]). The aim of these paper is to provide other useful… (More)