Concerning connectedness im kleinen and a related property

• Autorzy: R. L. Moore
• Języki publikacji: EN

Abstrakty

EN

Sierpinski has shown (Wacław Sierpiński Sur une condition pour qu'un continu soit une courbe jordanienne, Fundamenta Mathematicae I (1920), pp. 44-60) that in order that a closed and connected set of points M should be a continuous curve it is necessary and sufficient that, for every positive number ϵ, the connected point-set M should be the sum of a finite number of closed and connected point-sets each of diameter less than ϵ. It follows that, as applied to point-sets which are closed, bounded and connected, this property is equivalent to that of connectedness "im kleinen". The purpose of the present paper is to make a further study of these two properties (or rather suitable modifications of these properties) especially as applied to sets which are not necessarily closed.

Słowa kluczowe

PL

zbiór domknięty; zbiór spójny; spójność "im kleinen"; topologia; rodzina zbiorów

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1922
• Tom: 3
• Numer: 1
• Strony: 232-237

Daty

wydano

1922

Twórcy

autor

R. L. Moore

• Austin, U.S.A.