Related papers: Automatic continuity of biseparating maps

We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This…

A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…

We prove that an injective map $f:X\to Y$ between connected metrizable spaces $X,Y$ is continuous if for every connected subset $C\subset X$ the image $f(C)$ is connected and one of the following conditions is satisfied: (1) $Y$ is a…

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.

We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…

We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on $\mathbb{R}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B} u$ is a measure. We also prove strict continuity of…

We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges…

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can…

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…

A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.

Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.

This paper is a continuation of work started in \cite{njampavcont} on preserving continuity in ideal topological spaces. We will deal with $\theta$-continuity and weak continuity and give their translations in ideal topological spaces. As…

We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic…

A fundamental open question asking whether all real-valued strongly quasiconvex functions defined on $\mathbb R^n$ are necessarily continuous, akin to their convex counterparts, is answered in detail in this paper. Among other things, we…

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

We characterize locally injective semialgebraic maps between two semialgebraic sets in terms of the induced homomorphism between their rings of (continuous) semialgebraic functions.