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.
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.
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...
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