The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.

Given a Hausdorff uniform space $$X$$ with the countable gage of pseudometrics uniformity , we introduce concept approximate variation function $$f$$ mapping subset $$T$$ reals into : this is infimum family Jordan-type variations all functions $$g:T\to X$$ which differ from in each pseudometric, generated by pseudometric gage, not greater than $$\varepsilon>0$$ . We prove following compactness ...

Consider a maximal amenable subgroup H in a discrete countable group G. In this talk I will give a general condition implying that the von Neumann subalgebra LH is still maximal amenable inside LG. The condition is expressed in terms of H-invariant measures on some compact G-space. As an example I will show that the subgroup of upper triangular matrices inside SL(n,Z) gives rise to a maximal am...

First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretat...

Inspired by a recent paper due to José Luis García, we revisit the attempt of Daniel Simson construct counterexample pure semisimplicity conjecture. Using compactness, show that existence such would readily follow from very certain (countable set of) hereditary artinian rings finite representation type. The is then proved be equivalent special types embeddings, which call tight, division into s...

Suppose for simplicity that T is first order with Skolem functions in strong enough sense. We prove, in ZFC, that is has a model B in which for any two atomless Boolean algebras definable in it, any isomorphism or even complete embedding from one to the other is definable in the model. This has consequences on the compactness of logics gotten by extending first order logic by quantifying over s...

A group G is non-topologizable if the only Hausdorff group topology that G admits is the discrete one. Is there an infinite group G such that H/N is non-topologizable for every subgroup H ≤ G and every normal subgroup N ⊳ H? We show that a solution of this essentially group theoretic question provides a solution to the problem of c-compactness. Following Ol'shanskiˇı, we say that a group G is n...

This note is meant to clarify the relation between different commonly used definitions of proper discontinuity without the local compactness assumption for the underlying topological space. Much of the discussion applies to actions of nondiscrete topological groups, but, since my primary interest is geometric group theory, I will work only with discrete groups. Throughout this note, I will be w...

This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...

Countable compactifications of topological spaces have been studied in [1], [5], [7], and [9]. In [7], Magill showed that a locally compact, T2 topological space X has a countable T2 compactification if and only if it has n-point T2 compactifications for every integer n ≥ 1. We generalize this theorem to T2-ordered compactifications of ordered topological spaces. Before starting our generalizat...