HIERARCHY OF CURVES WITH WEAKLY CONFLUENT MAPS

被引：0

作者：

Illanes, Alejandro ^{[1
]}

Martinez-de-la-Vega, Veronica ^{[1
]}

Martinez-Montejano, Jorge M. ^{[2
]}

Michalik, Daria ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[2] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City 04510, DF, Mexico

[3] Jan Kochanowski Univ, Dept Math, PL-25406 Kielce, Poland

来源：

COLLOQUIUM MATHEMATICUM | 2023年 / 174卷 / 02期

关键词：

continuum; confluent; dendrite; Gehman dendrite; monotone; universal dendrite; weakly confluent; CLASSIFICATION; MAPPINGS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given continua X, Y and a class F of maps between continua, define X >=(F) Y if there exists an onto map f : X -> Y belonging to F. A map f : X -> Y is weakly confluent if for each subcontinuum B of Y, there exists a subcontinuum A of X such that f(A) = B. In this paper we consider the class W of weakly confluent maps. We study the hierarchy of curves with respect to the partial order <=(W). Two continua X and Y are W-equivalent provided that X <=(W) Y and Y <=(W) X. A continuum X is W-isolated provided that the following implication holds: if Y is a continuum and X and Y are W-equivalent, then X and Y are homeomorphic. Among other results, (a) we study how the class of dendrites with finite set of ramification points behaves under <=(W), (b) using <=(W), we compare dendrites with other curves, (c) we characterize W-isolated finite graphs.

引用

页码：241 / 255

页数：15