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Dwie Warszawy - zbiory dwuspójne: historia niedokończona

Jerzy Mioduszewski — 2007

Antiquitates Mathematicae

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.

Mosty królewieckie

Jerzy Mioduszewski — 2008

Antiquitates Mathematicae

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...

On continuous self-maps and homeomorphisms of the Golomb space

Taras O. BanakhJerzy MioduszewskiSławomir Turek — 2018

Commentationes Mathematicae Universitatis Carolinae

The Golomb space τ is the set of positive integers endowed with the topology τ generated by the base consisting of arithmetic progressions { a + b n : n 0 } with coprime a , b . We prove that the Golomb space τ has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set Π of prime numbers is a dense metrizable subspace of τ , and each homeomorphism h of τ has the following properties: h ( 1 ) = 1 , h ( Π ) = Π , Π h ( x ) = h ( Π x ) , and h ( x ) = h ( x ) for all x . Here x : = { x n : n } and Π x denotes the set of prime divisors...

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