Related papers: A concrete co-existential map that is not confluen…

We prove that the Cech-Stone remainder of the real line has a family of 2^c mutually non-homeomorphic subcontinua. We also exhibit a consistent example of a first-countable continuum that is not a continuous image of this remainder.

We answer a question of Juhasz by constructing under CH an example of a locally connected continuum without nontrivial convergent sequences.

We study chain-recurrence and chain-transitivity in compact dynamical systems without any regularity assumptions on the map. We prove that every compact system has a chain-recurrent point and a closed, invariant, chain-transitive subsystem.…

A general method for constructing sharply $k$-arc-transitive digraphs, i.e. digraphs that are $k$-arc-transitive but not $(k+1)$-arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples.…

In this article we give several examples of line bundles on certain non-compact surfaces that cannot be equipped with a flat connection.

We give a simple and explicit example of a complex Banach space which is not isomorphic to its complex conjugate, and hence of two real-isomorphic spaces which are not complex-isomorphic.

We show by (counter)example that the intersection of complemented submodules in a Hilbert $C^*$-module is not necessarily complemented, answering an open question from [MR].

Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact manifolds. In the case both manifolds are orientable, the theory holds for integer coefficients. The sheaf introduced here is stable to…

Indecomposable continua with one composant are $\textit{large}$ in the sense of being non-metrisable. We adapt the method of Smith $[18]$ to construct an example which is $\textit{small}$ in the sense of being separable.

We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and…

Let $g:\, [0, 1]\rightarrow [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $\psi:\, [0, 1]\rightarrow [0, 1]$ such that $g\circ \psi =…

A rational map between certain specific threefolds is given in an explicit manner.

This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…

We construct a family of 1-convex threefolds, with exceptional curve C of type (0,-2), which are not embeddable in C^m \times CP_n. In order to show that they are not Kaehler we exhibit a real 3-dimensional chain A whose boundary is the…

We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…

We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also…

We study the geometry and topology of real analytic maps $\mathbb{C}^n \to \mathbb{C}^k$, where $n > k$, regarded as mixed maps, defined below. Firstly, we give two natural families of mixed isolated complete intersection singularities,…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…

Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment,…

By studying periodic points for rational maps on $\bm{C}^d$ with $p$ invariants, we show that they form an invariant variety of dimension $p$ if the periodicity conditions are `fully correlated', and a set of isolated points if the…