Related papers: The structures of pointwise recurrent quasi-graph …

The results obtained in this paper grew from an attempt to generalize the main theorem of [1]. There it was shown that any circuit injection (a 1-1 onto edge map f such that if C is a circuit then f(C) is a circuit) from a 3-connected, not…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

A function $f:X\to \mathbb R$ defined on a topological space $X$ is called returning if for any point $x\in X$ there exists a positive real number $M_x$ such that for every path-connected subset $C_x\subset X$ containing the point $x$ and…

Let $ R $ be a rational map with totally disconnected Julia set $ J(R). $ If the postcritical set on $ J(R) $ contains a non-persistently recurrent (or conical) point, then we show that the map $ R $ can not be a structurally stable map.

A simple topological graph is $k$-quasiplanar ($k\geq 2$) if it contains no $k$ pairwise crossing edges, and $k$-planar if no edge is crossed more than $k$ times. In this paper, we explore the relationship between $k$-planarity and…

Consider a multimodal interval map $f$ of $C^3$ with non-flat critical points. We establish several characterizations of the map $f$ is quasi-symmetrically conjugated to a piecewise affine map in the case $f$ is topologically exact and all…

We define recurrence for a compactly generated para-topological group $G$ acting continuously on a locally compact Hausdorff space $X$ with $\dim X=0$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i)…

Let $E,F$ be two topological spaces and $u:E\rightarrow F$ be a map. \ If $F$ is Haudorff and $u$ is continuous, then its graph is closed. \ \ The Closed Graph Theorem establishes the converse when $E$ and $F$ are suitable objects of…

If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…

For a $2$-connected graph $G$ and vertices $u,v$ of $G$ we define an abstract graph $\mathcal{P}(G_{uv})$ whose vertices are the paths joining $u$ and $v$ in $G$, where paths $S$ and $T$ are adjacent if $T$ is obtained from $S$ by replacing…

We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z^2 by removing all horizontal edges off the X-axis,…

A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, these graphs are studied by presenting some examples and defining some of their sub-structures such as removable…

We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…

Let $f$ be a chain mixing continuous onto mapping from the Cantor set onto itself.Let $g$ be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate $f$ in the topology of…

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…

In the following text we show if $X$ is an Alexandroff space, then $f:X\to Y$ has closed graph if and only if it has constant closed value on each connected component of $X$. Moreover, if $X$ an Alexandroff space and $f:X\to Y$ has closed…

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such…

A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every…

Let $\phi:\mathcal{C}(S)\to\mathcal{C}(S')$ be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation $S$ and $S'$ are homeomorphic and $\phi$ is induced by a…

In this paper, we obtain a characterizations of the recurrence of a continuous vector field $w$ of a closed connected surface $M$ as follows. The following are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is pointwise almost periodic.…