Tychonoff spaces are named after AndreyNikolayevichTychonoff, whose Russian name (Тихонов) is also sometimes transliterated as "Tychonov", "Tikhonov", "Tihonov", or "Tichonov".
Tychonoff spaces are precisely those topological spaces which can be embedded in a compact Hausdorff space.
More precisely, for every Tychonoff space X, there exists a compact Hausdorff space K and an injective continuous map j from X to K such that the inverse of j is also continuous.
AndreyNikolayevichTychonoff (Russian: Андрей Николаевич Тихонов) (October 30, 1906, Gzhatsk – November 8, 1993, Moscow) was a Russian mathematician.
He is best known for his work on topology, including the metrization theorem he proved in 1926, and the Theorem of Tychonoff which states that every product of arbitrarily many compact topological spaces is again compact.
Tychonoff received numerous honors and awards for his work, lincluding the Lenin Prize (1966) and the Hero of Socialist Labor (1954, 1986).
The most common way, other than Andrei Nikolaevich Tikhonov, is to write it as AndreyNikolayevichTychonoff.
Andrei Nikolaevich Tikhonov attended secondary school as a day pupil and entered the Moscow University in 1922, the year in which he completed his school education.
His studied in the Mathematics Department of the Faculty of Mathematics and Physics at Moscow University and made remarkable progress, having his first paper published in 1925 while he was still in the middle of his undergraduate course.
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AndreyNikolayevichTychonoff (Андрей Николаевич Тихонов: October 30, 1906 – 1993) was a Russia n mathematician.
Tikhonov regularization, one of the most widely used methods to solve inverse problem s, is named in his honour.
He is best known for his work on topology, including the Metrization theorems he proved in 1926, and the Tychonoff's theorem which states that every product of arbitrarily many Compact space Topological space is again Compact space.
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For example, they are Hausdorff space paracompact spaces (and hence normal space and Tychonoff space) and first countable.
(Historical note: The form of the theorem shown here was in fact proved by AndreyNikolayevichTychonoff in 1926.
What Pavel Samuilovich Urysohn had shown, in a paper published posthumously in 1925, was the slightly weaker result that every second-countable normal space Hausdorff space is metrizable.) Several other metrization theorems follow as simple corollaries to Urysohn's Theorem.
