Publication Date

8-2018

Date of Final Oral Examination (Defense)

5-3-2012

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Marion Scheepers, Ph.D.

Supervisory Committee Member

Liljana Babinkostova, Ph.D.

Supervisory Committee Member

Andrés Caicedo, Ph.D.

Abstract

Screenability and strong screenability were both introduced some sixty years ago by R.H. Bing in his paper Metrization of Topological Spaces. Since then, much work has been done in exploring selective screenability (the selective version of screenability). However, the corresponding selective version of strong screenability has been virtually ignored. In this paper we seek to remedy this oversight. It is found that a great deal of the proofs about selective screenability readily carry over to proofs for the analogous version for selective strong screenability. We give some examples of selective strongly screenable spaces with the primary example being Pol's space. We go on to explore a natural weakening of selective strong screenability in topological groups. We conclude with an exploration of the difficulty in extending discrete families of sets as well as giving several directions one might go in when continuing the exploration of selective strong screenability.

DOI

10.18122/td/1428/boisestate

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