Related papers: Topological equivalence to a projection

Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

A standard procedure in classical projective geometry, using pencils of lines to extend an incidence plane to a projective plane, is examined from a constructive viewpoint. Brouwerian counterexamples reveal the limitations of traditional…

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high…

We introduce notions of suspension and flow equivalence on one-sided topological Markov shifts, which we call one-sided suspension and one-sided flow equivalence, respectively. We prove that one-sided flow equivalence is equivalent to…

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.

We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…

For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…

We formulate a relative, representation theoretic, notion of the algebraic cone construction. This motivates a generalization of the cone corresponding to a preprojective algebra.

We analyze and compare different dynamical systems and groupoids which can be obtained from projection point patterns. We define the cohomology of a point pattern as the cocycle cohomology of the pattern groupoid. We describe this…

This short note introduces a notion of directed homotopy equivalence and of "directed" topological complexity (which elaborates on the notion that can be found in e.g. Farber's book) which have a number of desirable joint properties. In…

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…

In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in $\mathbb{P}^{n+1}_k$, the cyclic $d$-fold cover $\widetilde{Y} \to \mathbb{P}^{n+1}_k$ branched along $Y$ completely characterizes $Y$ up to projective…

We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism…

We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…

We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…