In [5], a representation of bounded lattices within so-called standard topological contexts has been developed. Based on the theory of formal concept analysis [14] it includes Stone’s representation of Boolean algebras by totally disconnected compact spaces [10], Priestley’s representation of bounded distributive lattices by totally order disconnected compact spaces [7] as well as Urquhardt’s r...

Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected. Bishop defines a metric space to be compact if it is complete and totally bounded. A subset of a totally bounded set...

We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group SN. The problem is closely related to the theory of characters and factor representations of gro...

We enumerate all totally real number fields F with root discriminant δF ≤ 14. There are 1229 such fields, each with degree [F : Q] ≤ 9. In this article, we consider the following problem. Problem 1. Given B ∈ R>0, enumerate the set NF (B) of totally real number fields F with root discriminant δF ≤ B, up to isomorphism. To solve Problem 1, for each n ∈ Z>0 we enumerate the set NF (n,B) = {F ∈ NF...

A Polish group is locally Roelcke precompact if there a neighborhood of the identity element that totally bounded in (or lower) uniformity. These form subclass groups, while generalizing and compact groups.

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

In this paper, we prove that if every totally real bisectional curvature of an n(≥ 3)-dimensional complete Kähler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than c 4(n2−1)n(2n− 1), then it is totally geodesic. Mathematics Subject Classifications: 53C50, 53C55, 53C56.

Hart, K.P. and J. van Mill, Discrete sets and the maximal totally bounded group topology, Journal of Pure and Applied Algebra 70 (1991) 73-80. If G is an Abelian group, then G # is G with its maximal totally bounded group topology. We prove that every A c G# contains a closed (in G#) and discrete subset B such that lB1 = IAl. This answers a question posed by Eric van Douwen. We also present an ...

In this paper, we establish the following result: Let M be an n-dimensional complete totally real minimal submanifold immersed in CPn with Ricci curvature bounded from below. Then either M is totally geodesic or infr ≤ (3n+1)(n−2)/3, where r is the scalar curvature of M .