A collection of notes on frames

A collection of notes on frames

I first became interested in frames around 1974. Since then I have been writing notes on frames and associated topics. Most of these have been rather haphazard; designed to help me understand a particular aspect of the subject rather than as part of a coherent account.

A few years ago, say 2000, I started to write a more systematic account. This took the form of various sets of notes on chunks of the subject. My intention was aways to make these publicly available, but at first I had a vain hope (or perhaps it was a vane hope, so perhaps we shouldn't continue in that vein) that these notes should be more or less finished before they were released from captivity.

Around 2005, or perhaps a bit earlier, people began to ask me how the project was going, could they see what was written, and so on. Thus I decided to clean up what had been written and put those notes on my web pages, with a promise of more to come. The first set was made available on 30 June 2006.

As I said, there are various sets of notes. Let me call each such set a part. Each part has been written separately, with some references to other parts, and with some overlap with other parts. Thus I have not tried to organize the whole collection as I would a book. I may have unintentionally omitted certain topics, so I have given myself the option of amending one part without having to worry about what happens to the other parts. Some omission may need a whole new part to be written, and almost certainly that would have overlaps with other parts.

The parts are not intended to form a linear sequence, nor are they intended to form a comprehensive account of the whole subject. The first three parts

Basics Assembly Point space
contain mostly essential information for anyone interested in the subject. Thereafter I have concentrated on those topics that interest me, and know about.

Here is a list of the available parts, and projected parts. There are links to those parts that are available. I have also included an overview of the whole projected collection. I suggest you have a look at that before you dip into any particular part.

  • Overview -- Z-Overview.dvi or Z-Overview.ps or Z-Overview.pdf
  • The basics of frame theory -- A-Basics.dvi or A-Basics.ps or A-Basics.pdf
  • The assembly of a frame -- B-Assembly.dvi or B-Assembly.ps or B-Assembly.pdf
  • The point space of a frame -- C-POINTSPACE.dvi or C-POINTSPACE.ps or C-POINTSPACE.pdf
  • The fundamental triangle of a space -- D-FUNDTRIANGLE.dvi or D-FUNDTRIANGLE.ps or D-FUNDTRIANGLE.pdf
  • Boolean reflections of frames
  • The higher level CB properties of frames
  • Examples of higher level assemblies
  • The localic approach to boolean reflections