Related papers: D-forced spaces: a new approach to resolvability
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally…
We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the…
We present a broad and simple class of scalar-tensor scenarios that successfully realize dynamical damping of the effective cosmological constant, therefore providing a viable dynamical solution to the fine-tuning or "old" cosmological…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
We prove that a metric measure space $(X,d,m)$ satisfying finite dimensional lower Ricci curvature bounds and whose Sobolev space $W^{1,2}$ is Hilbert is rectifiable. That is, a $RCD^*(K,N)$-space is rectifiable, and in particular for…
We develop domain theory in constructive univalent foundations without Voevodsky's resizing axioms. In previous work in this direction, we constructed the Scott model of PCF and proved its computational adequacy, based on directed complete…
The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a…
Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces…
A novel exactly solvable Schr\"odinger equation with a position-dependent mass (PDM) describing a Coulomb problem in $D$ dimensions is obtained by extending the known duality relating the quantum $d$-dimensional oscillator and…
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
In 1984, Ditor asked two questions: (1) For each $n\in\omega$ and infinite cardinal $\kappa$, is there a join-semilattice of breadth $n+1$ and cardinality $\kappa^{+n}$ whose principal ideals have cardinality $< \kappa$? (2) For each $n \in…
S. Donaldson introduced a metric on the space of volume forms, with fixed total volume on any compact Riemmanian manifold. With this metric, the space of volume forms formally has non-positive curvature. The geodesic equation is a fully…
A weighted Hilbert space $F^2_{\varphi}$ of entire functions of $n$ variables is considered in the paper. The weight function $\varphi$ is a convex function on ${\mathbb C}^n$ depending on modules of variables and growing at infinity faster…
This paper proposes a construction of $C^r$ conforming finite element spaces with arbitrary $r$ in any dimension. It is shown that if $k \ge 2^{d}r+1$ the space $\mathcal P_k$ of polynomials of degree $\le k$ can be taken as the shape…
In this paper we prove that the space $\cM(n,\rv,D,\Lambda):=\{(M^n,g) \text{ closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and } \int_{M}|\Rm|^{n/2}\le \Lambda\}$ has at most $C(n,\rv,D,\Lambda)$ many diffeomorphism…
We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We demonstrate the capabilities of probabilistic diffusion models to reduce dramatically the computational cost of expensive hydrodynamical simulations to study the relationship between observable baryonic cosmological probes and dark…
We introduce the notion of echeloned spaces - an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly…