JordiGHBesides Tikhonov regularisation (French transliteration) and Tychonoff's theorem (German transliteration) do we have another instance of a mathematician whose name is commonly spelled two different ways for two different results?
xameer- a space is compact if and only if every family of closed subsets having the finite intersection property has non-empty intersection.
This formulation of #compactness is used in some proofs of #Tychonoff's theorem and the #uncountability of the real numbers
This formulation of #compactness is used in some proofs of #Tychonoff's theorem and the #uncountability of the real numbers
- A net inproduct space has a limit iff each projection has a limit. Symbolically, if (xα) is a net in the product X = πiXi, then it converges to x if and only if {\pi _{i}(x_{\alpha })\to \pi _{i}(x)} for each i. With compactness in terms on nets ->proof of #Tychonoff's theorem
- The compactness theorem for the propositional calculus is a consequence of #Tychonoff's theorem (which says that the product of compact spaces is compact) applied to compact Stone spaces
That's democratic socialist
That's democratic socialist
Colin the Mathmo@amiloradovsky As I recall, #Tychonoff's theorem is equivalent to AC. My posts won't be going there, these are intended for kids in a maths club, so #topology is probably a step too far.
But it is interesting.