Related papers: A lattice-theoretic approach to arbitrary real fun…
Let I be a dense linear order with a left endpoint but no right endpoint. We consider the lattice L(I) of finite unions of closed intervals of I. This lattice arises naturally in the setting of o-minimality, as these are precisely the…
In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
We develop a hierarchy of semilattice bases (S-bases) for frames. For a given (unbounded) meet-semilattice $A$, we analyze the interval in the coframe of sublocales of the frame of downsets of $A$ formed by all frames with the S-base $A$.…
There exist lattice actions which give cut--off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant…
We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal…
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…
The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal…
When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for…
We introduce a real vector space composed of set-valued maps on an open set X and note it by S. It is a complete metric space and a complete lattice. The set of continuous functions on X is dense in S as in a metric space and as in a…
We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating…
This paper deals with lattices $(L,\Vert~\Vert)$ over polynomial rings, where $L$ is a finitely generated module over $k[t]$, the polynomial ring over the field $k$ in the indeterminate $t$, and $\Vert~\Vert$ is a discrete real-valued…
We introduce a general unifying framework for the investigation of pointlike sets. The pointlike functors are considered as distinguished elements of a certain lattice of subfunctors of the power semigroup functor; in particular, we exhibit…
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such…
The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined…
We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integration of the square of the norm of the tangential derivative,…
We study rings of real-valued continuous functions in terms of pseudocomplementation conditions on various lattices attached to their prime spectrum. We fully characterize pseudocomplementation in all cases and have an almost complete…
We generalize the concept of the pointwise supremum of real-valued functions to the pointfree setting. The concept itself admits a direct and intuitive formulation which makes no mention of points. But our aim here is to investigate…