- Tytuł:
- Closed connected sets which remain connected upon the removal of certain, connected subsets
- Autorzy:
- Kline, John
- Powiązania:
- https://bibliotekanauki.pl/articles/1385777.pdf
- Data publikacji:
- 1924
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
zbiór spójny
krzywa Jordana
krzywa zamknięta
krzywa
podzbiór właściwy
topologia - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1924, 5, 1; 3-10
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł