There is a deeper preparation theorem for smooth functions, due to bernard malgrange, called the malgrange preparation theorem. We classify the computational content of the bolzanoweierstrass theorem and variants thereof in the weihrauch lattice. We present a short proof of the bolzano weierstrass theorem on the real line which avoids monotonic subsequences, cantors intersection theorem, and the heineborel. Schep at age 70 weierstrass published the proof of his wellknown approximation theorem. Ciao vila994, lenunciato del teorema di weierstrass.
Pdf the celebrated and famous weierstrass approximation theorem characterizes the set of continuous functions on a compact interval. In mathematics, specifically in real analysis, the bolzanoweierstrass theorem, named after. The stoneweierstrass theorem throughoutthissection, x denotesacompacthaus. At age 70 weierstrass published the proof of his wellknown approximation. Despite leaving university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnastics. Pdf a short proof of the bolzanoweierstrass theorem.
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