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Stone-Weierstrass: proof, part 1
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In this lecture Roland Speicher (Saarland University) discusses and proves the Theorem of Stone-Weierstrass, which says that a unital subalgebra of C(K) which separates points of K is dense in C(K).
The lecture is divided into 8 small videos; in this sixth video, the proof of the theorem is started. It is shown how we can approximate a function in C(K) by an element from our subalgebra. This approximation is done in two steps, first one has to make sure that the function approximates from below, in the second step one has to improve this to also approximation from above. Here the first step is presented, the second step will be done in the next video.
The lecture is divided into 8 small videos; in this sixth video, the proof of the theorem is started. It is shown how we can approximate a function in C(K) by an element from our subalgebra. This approximation is done in two steps, first one has to make sure that the function approximates from below, in the second step one has to improve this to also approximation from above. Here the first step is presented, the second step will be done in the next video.
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