Extended topology: connected sets and Wallace separations
Hammer, Preston C. (1963)
Portugaliae mathematica
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Displaying similar documents to “Co-Connected Spaces”
Extended topology: connected sets and Wallace separations
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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,...
On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets is connected.
Tzannes, V. (1998)
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A theorem concerning connected point sets
John Kline (1922)
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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.