Related papers: The Collins-Roscoe mechanism and D-spaces
In this paper, the concepts of $K$-subset systems and $k$-well-filtered spaces are introduced, which provide another uniform approach to $d$-spaces, $s$-well-filtered spaces (i.e., $\mathcal{U}_{S}$-admissibility) and well-filtered spaces.…
We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…
We give a concise proof of a classification of lens spaces up to orientation-preserving homeomorphisms. The chief ingredient in our proof is a study of the Alexander polynomial of ` symmetric' links in $S^3$.
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…
It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis…
We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on…
It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general.…
We show that the ideal of an arrangement of d linear subspaces of projective space is d-regular in the sense of Castelnuovo and Mumford, answering a question of B. Sturmfels. In particular this implies that the ideal of an arrangement of d…
A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way…
Let X be an irreducible reduced complex space on which a connected compact Lie group K acts by holomorphic automorphisms. Let G be the complexification of K and g the Lie algebra of G. Following the theory of algebraic transformation…
We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a…
We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…
Apart from simply-connected spaces, a non simply-connected co-H-space is a typical example of a space X with a co-action of $B\pi_1(X)$ along $r^X : X \rightarrow B\pi_{1}(X)$ the classifying map of the universal covering. If such a space X…
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact $R$-linear functor between $R$-linear tensor-triangulated categories which are rigidly-compactly…
We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator $\mathbf{T}$ that is singular of order $r_0\in[0,2]$. For $r_0\in(0,1]$ we prove well-posedness in Gevrey spaces $G^s$ with…
Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $\sH$ with a multivalued part $\mul A$. An operator $B$ in $\sH$ with $\ran B\perp\mul A^{**}$ is said to be an operator part of $A$ when $A=B \hplus (\{0\}\times \mul…
A surface in Euclidean space $\r^3$ is said to be an $\alpha$-stationary surface if it is a critical point of the energy $\int_\Sigma|p|^\alpha$, where $\alpha\in\r$. We prove that all ruled $\alpha$-stationary surfaces are vector planes…
In recent decades, linear affine threefolds have enabled researchers to solve some of the challenging problems on affine spaces. Koras-Russell threefolds, especially the Russell Cubic over $\mathbb{C}$ and Asanuma threefolds over a field of…
A space is called linearly H-closed iff any chain cover possesses a dense member. This property lies strictly between feeble compactness and H-closedness. While regular H-closed spaces are compact, there are linearly H-closed spaces which…
Consider a linear space L of complex D-dimensional linear operators, and assume that some power L^k of L is the whole space of DxD matrices. Perez-Garcia, Verstraete, Wolf and Cirac conjectured that the sequence L^1,L^2,... stablilizes…