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  1. 4 Fundamenta Mathematicae

Autorzy help

  1. 4 Kline J. R.

Lata help

  1. 1 1927

  2. 1 1925

  3. 1 1924

  4. 1 1922

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A theorem concerning connected point sets

100%
Kline J. R.
Fundamenta Mathematicae
|
1922
|
tom 3
|
nr 1
238-239
EN
The purpose of the present note is to show that no connected point set can have more than one point such that when it is removed, the reminder is totally disconnected.
2
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Closed connected sets which remain connected upon the removal of certain, connected subsets

100%
Kline J. R.
Fundamenta Mathematicae
|
1924
|
tom 5
|
nr 1
3-10
EN
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.
3
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Concerning the sum of two continua each irreducible between the same pair of points

100%
Kline J. R.
Fundamenta Mathematicae
|
1925
|
tom 7
|
nr 1
314-322
EN
The first part of the paper answers the question whether two different continua, each irreducible between the same pair of points could have a sum irreducible between two of its points. The second part shows certain properties of continua irreducible between the same pair of points and having the above mentioned property with respect to their sum.
4
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A condition that every subcontinu of a continuous curve be a continuous curve

50%
Kline J. R.
Fundamenta Mathematicae
|
1927
|
tom 10
|
nr 1
298-301
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