# Concerning connectedness im kleinen and a related property

Fundamenta Mathematicae (1922)

• Volume: 3, Issue: 1, page 232-237
• ISSN: 0016-2736

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## Abstract

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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.

## How to cite

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Moore, R.. "Concerning connectedness im kleinen and a related property." Fundamenta Mathematicae 3.1 (1922): 232-237. <http://eudml.org/doc/213292>.

@article{Moore1922,
abstract = {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.},
author = {Moore, R.},
journal = {Fundamenta Mathematicae},
keywords = {zbiór domknięty; zbiór spójny; spójność "im kleinen"; topologia; rodzina zbiorów},
language = {eng},
number = {1},
pages = {232-237},
title = {Concerning connectedness im kleinen and a related property},
url = {http://eudml.org/doc/213292},
volume = {3},
year = {1922},
}

TY - JOUR
AU - Moore, R.
TI - Concerning connectedness im kleinen and a related property
JO - Fundamenta Mathematicae
PY - 1922
VL - 3
IS - 1
SP - 232
EP - 237
AB - 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.
LA - eng
KW - zbiór domknięty; zbiór spójny; spójność "im kleinen"; topologia; rodzina zbiorów
UR - http://eudml.org/doc/213292
ER -

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