On σ-discrete coverings consisting of connected sets
Teodor Przymusiński (1973)
Colloquium Mathematicae
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Displaying similar documents to “A nondegenerate σ-discrete Moore space which is connected”
On σ-discrete coverings consisting of connected sets
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Sierpinski has shown (Wacław Sierpiński Sur une condition pour qu'un continu soit une courbe jordanienne, Fundamenta Mathematicae I (1920), pp. 44-60) that in order that a closed and connected set of points M should be a continuous curve it is necessary and sufficient that, for every positive number ϵ, the connected point-set M should be the sum of a finite number of closed and connected point-sets each of diameter less than ϵ. It follows that, as applied to point-sets which are closed,...
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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.
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