The Baire Category Theorem for complete metric spaces

My latest screencast is a lecture from G14FUN Functional Analysis where I prove the Baire Category Theorem for complete metric spaces: a countable intersection of dense, open subsets of a complete metric space must be dense.

The screencast is available from
http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-010210/

This screencast includes a picture-in-picture (PIP) of me in the bottom right hand corner along with the audio and the screen-capture movie from my tablet laptop. I am quite pleased with the way the PIP has come out this time. The webcam recorded this footage at 320×240 resolution, and I scaled it down slightly for the final production in Camtasia.

The audio quality is also improved from some recent screencasts: for some reason I had the microphone sensitivity setting in Camtasia set too high, and this was producing hiss and distortion.

Joel Feinstein
February 2 2010

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2 responses to “The Baire Category Theorem for complete metric spaces

  1. Emine Isceviren

    Thanks for the lecture. You explain Baire’s category theorem clearly and it was enjoyable to listen. I wish all my math professors explain math theorems and proofs in that way like you do; recalling the key lemmas and definitions is very important.

    Emine

    Like

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