Topologically maximal convergences, accessibility, and covering maps

Generating Topologically Correct Schematic Maps

This paper studies the creation of schematic maps from traditional vector-based, carto-graphic information. An algorithm is proposed to modify positions of lines in the original input map with the goal of producing as output a schematic map that meets certain geometric and aesthetic criteria. Special emphasis is placed here on preserving topological structure of features during this transformat...

Universal covering Maps and radial

Simplicial ramified covering maps

In this paper we define the concept of a ramified covering map in the category of simplicial sets and we show that it has properties analogous to those of the topological ramified covering maps. We show that the geometric realization of a simplicial ramified covering map is a topological ramified covering map, and we also consider the relation with ramified covering maps in the category of simp...

Topologically Constrained Segmentation with Topological Maps

This paper presents incremental algorithms used to compute Betti numbers with topological maps. Their implementation, as topological criterion for an existing bottom-up segmentation, is explained and results on artificial images are shown to illustrate the process.

The Classification of Topologically Expansive Lorenz Maps

We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive Lorenz map. A simple extension of the theorems to the case of expansive maps of the interval wit...