We identify four countable topological spaces S2, S1, SD, and S0 which serve as canonical examples of topological spaces which fail to be quasi-Polish. These four spaces respectively correspond to the T2, T1, TD, and T0-separation axioms. S2 is the space of rationals, S1 is the natural numbers with the cofinite topology, SD is an infinite chain without a top element, and S0 is the set of finite...

and Applied Analysis 3 The quasi-uniform space X,U will always be considered to be a topological space with the topology obtained by using as the family of all neighborhoods of a point x0 ∈ X all sets of the formU x0 {x ∈ X : x0, x ∈ U}, whereU runs overU. Such a topology is called topology of the quasi-uniformity. Note that each topology onX is induced by a quasi-uniformity see 8, 9 , the most...

A topological quasi-variety Q T ∼ ) := IScP + ∼ generated by a finite algebra ∼ with the discrete topology is said to be standard if it admits a canonical axiomatic description. Drawing on the formal language notion of syntactic congruences, we prove that Q T ∼ ) is standard provided that the algebraic quasi-variety generated by ∼ is a variety, and that syntactic congruences in that variety are...

We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame. These characterizations involve a special binary quasi-reachability relation on the dual structure; we call a point u a quasi-root of the dual structure if every ultrafilter is quasireachable from u. We prove that a bool...

The Luttinger surface of an organic metal (TTF-TCNQ), possessing charge order and spin-charge separated band dispersions, is investigated using temperature-dependent angle-resolved photoemission spectroscopy. The Luttinger surface topology, obtained from momentum distribution curves, changes from quasi-2D (dimensional) to quasi-1D with temperature. The high temperature quasi-2D surface exhibits...

The interpretation of auxiliary entities as boundary entities in previous non-manifold boundary (NMB) representations may change a model’s intended topology and increase the complexity of the corresponding data structure. In this paper, entities appearing in a modeling process are classified into boundary and non-boundary entities. Non-boundary entities are usually embedded into embeddingspace ...

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

Given A ⊆ ℝ , the Hattori space H(A) is topological ( τA ) where each a ∈ has -neighborhood base { − ε + : > 0 } and b [ . Thus, may be viewed as hybrid of Euclidean topology lower-limit topology. We investigate properties spaces well other topologies on using various combinations discrete, left-ray, lower-limit, upper-limit, topologies. Since these generated by quasi-metric ℝ, we quasi-metr...

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...

The Internet is unique. It is the most complex quasi-physical entity created by humans: we can’t completely model it, and we don’t fully understand its structure or its growth patterns [21]. As a result, hot research topics in the past several years include the empirical study of Internet topology, the construction of mathematical models of “Internet-like” topology [20, 1], problems in network ...