By Isbell duality, each compact regular frame L is isomorphic to the frame of opens of a compact Hausdorff space X. In this note we study the spectrum Spec(L) of prime filters of a compact regular frame L. We prove that X is realized as the minimum of Spec(L) and the Gleason cover of X as the maximum of Spec(L). We also characterize zero-dimensional, extremally disconnected, and scattered compa...

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

By sampling the window of a Gabor frame for L(R) belonging to Feichtinger’s algebra, S0(R), one obtains a Gabor frame for l(Z). In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces L(R), l(Z), L([0, L]) and C. Some new results about general dual windows with respect to sampling and per...

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

We give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is ...

We give a causal version of Eisenhart's geodesic characterization of Newtonian dynamics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is s...

The scalar-tensor theory is plagued by nagging questions if different conformal frames, in particular the Jordan and Einstein conformal frames, are equivalent to each other. As a closely related question, there are opposing views on which of the two conformal frames is physically acceptable. Reinforcing our previous claims, we offer replies based on a cosmological model of the scalar-tensor the...

Obviously each lattice that satisfies either (JID) or (MID) is distributive. A classic result in lattice theory is Funayama’s theorem [5] stating that there is an embedding e of L into a complete Boolean algebra B that preserves all existing joins and meets in L iff L satisfies both (JID) and (MID). Funayama’s original proof was quite involved. For complete L, Grätzer [6, Sec. II.4] gave a more...