相关论文: On finite-sheeted covering mappings onto solenoids

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…

We study slopes of finite cyclic covering fibrations of a fibered surface. We give the best possible lower bound of the slope of these fibrations. We also give the slope equality of finite cyclic covering fibrations of a ruled surface and…

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.

Solenoids induced by split sequences are introduced, as the inverse limit object of a sequence of fold maps. The topology of a solenoid is explored, and it is established that solenoids have naturally arising singular foliated structures.…

We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…

We survey recent developments on mapping class groups of surfaces of infinite topological type.

We define two classes of topological infinite degree covering maps modeled on two families of transcendental holomorphic maps. The first, which we call exponential maps of type $(p,q)$, are branched covers and is modeled on transcendental…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We answer two questions about the topology of end spaces of infinite type surfaces and the action of the mapping class group that have appeared in the literature. First, we give examples of infinite type surfaces with end spaces that are…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

A topological space is called a submetrizable if it can be mapped onto a metrizable topological space by a continuous one-to-one map. In this paper we answer two questions concerning sequence-covering maps on submetrizable spaces.

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…

A topological spherical space form is the quotient of a sphere by a free action of a finite group. In general, their homotopy types depend on specific actions of a group. We show that the monoid of homotopy classes of self-maps of a…

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…

Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface. For…

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…