For the study of some typical problems in finance and economics, Žitković introduced convex compactness gave many remarkable applications. Recently, motivated by random optimization variational inequalities, Guo, et al. L0-convex compactness, developed related theory normed modules further applied it to backward stochastic equations. In this paper, we extensively L0-convexly compact sets locall...

We study the large-scale geometry of mapping class groups surfaces infinite type, using framework Rosendal for coarse non locally compact groups. give a complete classification those whose have local boundedness (the analog compactness). When end space surface is countable or tame, we also where there exists coarsely bounded generating set finite generation, giving group well-defined quasi-isom...

We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higher-order variables. We show that this fragment enjoys the characteristic properties of first-order logic: complete proof systems, compactness, and countable models. We obtain these results with an analytic tableau system and a concomitant model ex...

We generalize D. Kelly’s and K.A. Nauryzbaev’s results of 1-variable and 2-variable equational compactness of complete distributive lattices satisfying the infinite distributive law and its dual (“bi-frames”) to objects similar to monadic algebras (which we will call projection algebras). This will lead us in particular to an example of bi-frame that is not 3-variable equationally compact, even...

1 ω Stable/Totally Transcendental Theories Throughout let T be a complete theory in a countable language L having infinite models. For an L-structure M and A ⊆ M let SM n (A) denote the set of n-types of A. We define a topology (called Stone topology) on SM n (A) by setting basic open sets to be of the form Uφ = {p ∈ SM n (A) : φ ∈ p} where φ is an L(A)-formula. Then SM n (A) is totally disconn...

We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zerodimensionality are shown to be equivalent. The part of this characterisation that concerns covering dimension extends to higher dimensions and to closed shrinkings of finite open covers. To deal with zero-dimensional subspaces uniformly, fo...

We study simple type theory with primitive equality (STT) and its first-order fragment EFO, which restricts equality and quantification to base types but retains lambda abstraction and higher-order variables. As deductive system we employ a cut-free tableau calculus. We consider completeness, compactness, and existence of countable models. We prove these properties for STT with respect to Henki...

The interplay between topological hyperconvex spaces and sigma-finite measures in such gives rise to a set of analytical observations. This paper introduces the Noetherian class k-finite k-hyperconvex subspaces (NHCs) admitting countable finite covers. A measure is constructed sigma-semiring NHC under ordering NHCs. relation maintains irreflexive anti-symmetric algebraic properties while retain...