Local connectedness of frames

In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5.

Grantor

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2004

Author dc:creator

• Mushaandja, Zechariah

Advisor dc:contributor.advisor

• Schauerte, Anneliese

• mathematics and applied mathematics

Handle dc:identifier.uri

http://hdl.handle.net/11427/38321

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/38321