Baire category theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 27/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Baire_category_theorem


00:00:21 1 Statement of the theorem
00:02:31 2 Relation to the axiom of choice
00:03:16 3 Uses of the theorem
00:05:00 4 Proof
00:08:56 5 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.994142677802071
Voice name: en-AU-Wavenet-A


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
The Baire category theorem (BCT) is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space.
The theorem was proved by René-Louis Baire in his 1899 doctoral thesis.