Related papers: Nbd is not cartesian closed

A compact space $K$ is {\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\cap\Sigma$ is dense in $K$, where $\Sigma$ is the sigma-product (= the set of points with countably many…

We study locally presentable categories equipped with a cofibrantly generated weak factorization system. Our main result is that these categories are closed under 2-limits, in particular under pseudopullbacks. We give applications to…

Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.

We show that the direct sum of uncountably many non-Abelian groups does not embed into the group of homeomorphisms of a compact metric space.

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which…

This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.

This note extends some recent results on the derived category of a geometric invariant theory quotient to the setting of derived algebraic geometry. Our main result is a structure theorem for the derived category of a derived local quotient…

We are checking the closed categories beginning with the category of sets and ending with the category of categories. The novelty is a generalizing the notion of adjoint functors to the joint pair of functors in the category of directed…

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.

Inspired by a work of Kapranov, we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via complex…

We show that on the unit ball of a certain separable Banach space there is a smooth delbar-closed (0,1)-form which is not locally delbar-exact. Further, the Dolbeault isomorphism theorem does not generalize to arbitrary Banach spaces.…

We show that for n $\ge$ 2 the space of closed n-cycles in a strongly (n -- 2)-concave complex space has a natural structure of reduced complex space locally of finite dimension and represents the functor "analytic family of n-cycles"…

We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian manifold which is not homotopy equivalent to any finite…

In this paper we prove generic results concerning Hardy spaces in one or several complex variables. More precisely, we show that the generic function in certain Hardy type spaces is totally unbounded and hence non-extentable, despite the…

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.

We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.

In this article we make the concept of a continuous family of triangles precise and prove the moduli functor classifying oriented triangles admits a fine moduli space but the functor classifying non-oriented triangles only admits a coarse…

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…

The boundary of the region in spacetime containing future-trapped closed surfaces is considered. In asymptotically flat spacetimes, this boundary does not need to be the event horizon nor a dynamical/trapping horizon. Some properties of…

There has been interest recently concerning when a left ordered group is locally indicable. Bergman and Tararin have shown that not all left ordered groups are locally indicable, but all known examples contain a nonabelian free subgroup. We…