相关论文: Compactness of Loeb Spaces
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
In this paper we are going to discuss compactness in Lorentz sequence spaces. Firstly, it will be shown how to define such a space, check whether a sequence belongs to it and calculate its norm. Equipped with this knowledge, we will proceed…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…
In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and…
Given a compact space in a fixed universe of set theory, one can naturally define its interpretation in any ZFC extension of the universe. We investigate the stability of some classes of compact spaces with respect to extensions of this…
We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…
An $\omega_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $\omega_1$-compact space is $\sigma$-countably compact, i.e., the union of…
We relativize the notion of a compact object in an abelian category with respect to a fixed subclass of objects. We show that the standard closure properties persist to hold in this case. Furthermore, we describe categorical and…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
In section 1 of this paper, we characterize the isomorphism property of nonstandard universes in terms of the realization of some second--order types in model theory. In section 2, several applications are given. One of the applications…
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing…
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under…
We discuss some well-known compactness principles for uncountable structures of small regular sizes ($\omega_n$ for $2 \le n<\omega$, $\aleph_{\omega+1}$, $\aleph_{\omega^2+1}$, etc.), consistent from weakly compact (the size-restricted…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
We study the bound on the compactness of a stellar object in pure Lovelock theories of arbitrary order in arbitrary spacetime dimensions, involving electromagnetic field. The bound we derive for a generic pure Lovelock theory, reproduces…
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to which subsequence of an ideal convergent sequence may fail to…
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than the size of the continuum.
We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of "every locally compact, perfectly normal space is paracompact".
We prove that it is consistent with large values of the continuum that there are no S-spaces. We also show that we can also have that compact separable spaces of countable tightness have cardinality at most the continuum.