# 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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topMoore, 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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