Related papers: A note on local properties in products
We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
In the present paper we study necessary and sufficient conditions for the existence of a semicontinuous and finite Richter-Peleg multi-utility for a preorder. It is well know that, given a preorder on a topological space, if there is a…
We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of…
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…
In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions. Under antisymmetry this property, also known as…
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different…
No convenient internal characterization of spaces that are productively Lindelof is known. Perhaps the best general result known is Alster's internal characterization, under the Continuum Hypothesis, of productively Lindelof spaces which…
The concept of a local infimum for an optimal control problem is introduced. This definition extends that of an optimal process. For a~local infimum we prove an existence theorem and derive necessary conditions that resemble some family of…
For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We…
We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only…
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
If E is a locally convex topological vector space, let P(E) be the pre-ordered set of all continuous seminorms on E. We study, on the one hand, for g an infinite cardinal those locally convex spaces E which have the g-neighbourhood property…
We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we…
We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…
We find sufficient conditions under which the product of spaces that have a $\pi$-tree also has a $\pi$-tree. These conditions give new examples of spaces with a $\pi$-tree: every at most countable power of the Sorgenfrey line and every at…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…
The topological condition for the existence of a $pin^c$ structure on the product of two Riemannian manifolds is derived and applied to construct examples of manifolds having the weaker Lipschitz structure, but no $pin^c$ structure. An…