Related papers: Uniformly Star Superparacompact Subsets and Spaces
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
Ultra compact stellar models with a two-zone uniform density equation of state are considered. They are shown to provide neat examples of optical geometries exhibiting double necks, implying that the gravitational wave potential has a…
We investigate star-covering properties of $\Psi$-like spaces. We show star-Lindel\"ofness is reflected by open perfect mappings. In addition, we offer a new equivalence of CH.
The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
In this paper, we provide an alternative description of the duality result for distributive lattices and coherent locales using ultraposet. In particular, we show that there are fully faithful embeddings from the opposite of the category of…
We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…
The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of…
This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested…
We describe the order type of range sets of compact ultrametrics and show that an ultrametrizable infinite topological space $(X, \tau)$ is compact iff the range sets are order isomorphic for any two ultrametrics compatible with the…
Motivated by the model theory of higher order logics, a certain kind of topological spaces had been introduced on ultraproducts. These spaces are called ultratopologies. Ultratopologies provide a natural extra topological structure for…
We find universal spaces for Alexandroff and finite spaces and explore some of its topological properties as well as their description as inverse limits of finite spaces and Alexandroff extensions. They can be used as a natural environment…
If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary…
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…
We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…
Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if $X$ is a countably compact space and $C_p(X)$ is a space of continuous functions in the pointwise topology…
We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…