5. Gelfand's problem revisited, mathematical curiosities and some open problems

Space-filling curves, Jordan arcs with positive area, non-trivial uniform algebras on the unit interval. Progress so far on Gelfand's problem concerning natural uniform algebras on the unit interval. Open problems from the whole course.

• The lecture notes as written in the lectures (PDF) – Slides 81 to 91

• Full podcast:
  
  • Slides 81 to 91 (Lecture 4; second half)

• Pauseless podcast (though quieter comments and questions may be lost):
  
  • Slides 81 to 91 (Lecture 4; second half)