Related papers: Pseudocompactness and the Uniform Metastability Pr…

The purpose of this paper is to generalize the variational principle, which states that the topological entropy is equal to the supremum of the measure theoretical entropies and also the minimum of the metric theoretical entropies, to…

We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style…

In aiming to apply to a broader class of examples the Avigad-Iovino "ultraproducts and metastability" approach to obtaining uniformity for convergence of sequences, we construct a framework using continuous logic that in particular is able…

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…

Using the new diffeomorphism invariants of Seiberg and Witten, a uniqueness theorem is proved for Einstein metrics on compact quotients of irreducible 4-dimensional symmetric spaces of non-compact type. The proof also yields a Riemannian…

We say that a topological space X is selectively sequentially pseudocompact (SSP for short) if for every sequence (U_n) of non-empty open subsets of X, one can choose a point x_n in U_n for every n in such a way that the sequence (x_n) has…

We introduce a new homology theory of uniform spaces, provisionally called $\mu$-homology theory. Our homology theory is based on hyperfinite chains of microsimplices. This idea is due to McCord. We prove that $\mu$-homology theory…

We prove a Model Existence Theorem for a fully infinitary logic for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson and…

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of…

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…

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

A novel selection principle was introduced by Dorantes-Aldama and Shakhmatov: a topological space $X$ is termed {\em selectively pseudocompact} if for any sequence $(U_n:n\in {\omega})$ of pairwise disjoint non-empty open sets of $X$, one…

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak…

A uniformly continuously integrable sequence of real-valued measurable functions, defined on some probability space, is relatively compact in the $\sigma(L^1,L^\infty)$ topology. In this paper, we link such a result to weak convergence…

For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if…

We introduce a covering notion depending on two cardinals, which we call $\mathcal O $-$ [ \mu, \lambda ]$-compactness, and which encompasses both pseudocompactness and many other generalizations of pseudocompactness. For Tychonoff spaces,…

Berestovskii and Plaut introduced the concept of a coverable uniform space when developing their theory of generalized universal covering maps for uniform spaces. Brodskiy, Dydak, LaBuz, and Mitra introduced the concept of a locally…

We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ and on the fundamental group $\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a topological space $X$ and use it to…

We show that for every compact 3-manifold $M$ there exists an open subset of $\diff ^1(M)$ in which every generic diffeomorphism admits uncountably many ergodic probability measures which are hyperbolic while their supports are disjoint and…