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

• Autorzy: John Robert Kline
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

PL

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1924
• Tom: 5
• Numer: 1
• Strony: 3-10

Daty

wydano

1924

Twórcy

autor

John Robert Kline

• Philadelphia, USA