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W poprzednim odczycie [1] akcentowana była wartość dowodów efektywnych w porównaniu z tymi, w których środkiem dowodowym jest pewnik wyboru. W tym odczycie będzie okazja przypomnieć, że pewnik wyboru pełni w sytuacjach mnogościowych rolę wyjaśniającą w odróżnieniu od konstrukcji efektywnych, które często mają charakter przypadkowości.
Latem 1734 kapitulował Gdańsk oblegany przez niemal dwa lata przez wojska rosyjskie interweniujące w Polsce przeciwko królowi Stanisławowi Leszczyńskiemu. Jednym z warunków kapitulacji było (patrz Sołowjew(1960)) wysłanie do Petersburga uroczystej deputacjizłożonej z najznakomitszych obywateli miasta, co nastąpiło w roku następnym. Wtedy to, według Kopielewicza(1977), burmistrz miasta, Carl Leonhard Gottlieb Ehler, spotkał się z Eulerem, przekazując mu zadanie o mostach królewieckich. O burmistrzu...
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set of prime numbers is a dense metrizable subspace of , and each homeomorphism of has the following properties: , , , and for all . Here and denotes the set of prime divisors...
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