Elements of Convergence Approach Theory

<p>We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Trott, William D

Contributors dc:contributor

• Jimmy Dillies
• Greg Michalski

• ETD
• Regularity
• Continuous extension
• Continuous convergence
• Other Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1095

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2115