The Baire Category Theorem - Dr Joel Feinstein

This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional Analysis.

See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the associated blog post at http://wp.me/posHB-7y In this screencast, Dr Feinstein proves the Baire Category Theorem for complete metric spaces - a countable intersection of dense, open subsets of a complete metric space must be dense.

This material is suitable for those with a knowledge of metric space topology and, in particular, dense subsets and complete metrics.

Category:

Education

Tags:

• Mathematics
• Math
• Maths
• Baire category theorem
• complete metric
• dense
• open
• topology
• metric space
• mathematics
• mathematical analysis
• functional analysis

[DasGewitter83]

Mr Feinstein thank you so much for these lectures, they really help me to understand these concepts!

[JoelFeinstein]

I agree that it would be good to have more space to write. However, readability is certainly improved when the data projector screen is large,

See my case studies on using IT to teach undergraduate maths for more of the arguments on both sides.

Note that putting all of the resulting materials on the web for the students is quite popular. Joel Feinstein

[sorrysonofa]

why does he not have a black board???? It's so much more fun...

Advantages of the blackboard: you have much more space than a single half sheet of paper, it's easier to manipulate.

Advantages of this method: readability, no dust.

I still prefer the blackboard, and I can hardly concentrate without one.