An open maps and span zero

• Main Author: Regacho, Corazon F.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Zero (The number); Mappings (Mathematics); Functions; Metric spaces; Topology; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1642; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8480/viewcontent/TG02362_F_Redacted.pdf
• Institution: De La Salle University

The span of a metric space is a measure of connectedness of the metric space. Defined by Duda and Lilek, this concept was studied intensively by McLean, Kawamura, Oversteegen and others. This paper presents some results by the above-named authors. The main result presented is the theorem which states that if a compactum has span zero, then its image under an open continuous map has span zero also. Among the concepts studied in this paper are the confluent maps between metric spaces and tree-like curves. Related to these are the approximately right invertible mappings and En-translations. All these concepts and their relations to spans of metric spaces are discussed in this paper.