# Closed connected sets which remain connected upon the removal of certain, connected subsets

Fundamenta Mathematicae (1924)

- Volume: 5, Issue: 1, page 3-10
- ISSN: 0016-2736

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topKline, John. "Closed connected sets which remain connected upon the removal of certain, connected subsets." Fundamenta Mathematicae 5.1 (1924): 3-10. <http://eudml.org/doc/213936>.

@article{Kline1924,

abstract = {The purpose of this paper is to prove: Theorem: Suppose M is a closed connected set containing more than one point such that if g is any connected subset of M, then M-g is connected. Under these conditions M is a simple closed curve. Theorem: If M is an unbounded closed connected set which remains connected upon the removal of any unbounded connected proper subset, then M is either an open curve, a ray of an open curve or a simple closed curve J plus OP, a ray of an open curve which has O and only O in common with J. Theorem: Suppose M is an unbounded closed connected set such that if g is any bounded connected subset of M, then M-g is connected. Then M is not a continuous curve.},

author = {Kline, John},

journal = {Fundamenta Mathematicae},

keywords = {zbiór spójny; krzywa Jordana; krzywa zamknięta; krzywa; podzbiór właściwy; topologia},

language = {eng},

number = {1},

pages = {3-10},

title = {Closed connected sets which remain connected upon the removal of certain, connected subsets},

url = {http://eudml.org/doc/213936},

volume = {5},

year = {1924},

}

TY - JOUR

AU - Kline, John

TI - Closed connected sets which remain connected upon the removal of certain, connected subsets

JO - Fundamenta Mathematicae

PY - 1924

VL - 5

IS - 1

SP - 3

EP - 10

AB - The purpose of this paper is to prove: Theorem: Suppose M is a closed connected set containing more than one point such that if g is any connected subset of M, then M-g is connected. Under these conditions M is a simple closed curve. Theorem: If M is an unbounded closed connected set which remains connected upon the removal of any unbounded connected proper subset, then M is either an open curve, a ray of an open curve or a simple closed curve J plus OP, a ray of an open curve which has O and only O in common with J. Theorem: Suppose M is an unbounded closed connected set such that if g is any bounded connected subset of M, then M-g is connected. Then M is not a continuous curve.

LA - eng

KW - zbiór spójny; krzywa Jordana; krzywa zamknięta; krzywa; podzbiór właściwy; topologia

UR - http://eudml.org/doc/213936

ER -

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