On confluent mappings

On Quasi-ω-Confluent Mappings

Hereditarily Weakly Confluent Mappings onto S

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...

Weakly Confluent Mappings and Finitely-generated Cohomology

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

∆k-Confluent and Ok-Confluent Graphs

In this paper we extend the concept of ∆-confluence to ∆k-confluence by allowing more generalized junctions, called ∆k-junctions. We present an algorithm for recognizing graphs that are ∆k-confluent. We then generalize ∆k-confluence to Ok-confluence by allowing non-intersecting chords within a junction, resulting in Ok-junctions. We present an algorithm for recognizing graphs that are Ok-conflu...

On Weakly Confluent Monadic String-Rewriting Systems

Madlener, K., P. Narendran, F. Otto and L. Zhang, On weakly confluent monadic string-rewriting systems, Theoretical Computer Science 113 (1993) 119-165. It is investigated as to how far the various decidability results for finite, monadic, and confluent string-rewriting systems can be carried over to the class of finite monadic string-rewriting systems that are only weakly confluent. Here a mon...