A nondegenerate σ-discrete Moore space which is connected
Peter de Caux (1979)
Colloquium Mathematicae
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Peter de Caux (1979)
Colloquium Mathematicae
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Katsuya Eda, Vlasta Matijević (2013)
Fundamenta Mathematicae
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Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and...
Tudor Ganea (1951)
Fundamenta Mathematicae
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S. K. Chatterjea (1969)
Matematički Vesnik
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S. K. Chatterjea (1968)
Matematički Vesnik
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J. Guthrie, H. Stone (1973)
Fundamenta Mathematicae
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Z. P. Mamuzić (1986)
Matematički Vesnik
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Hammer, Preston C. (1963)
Portugaliae mathematica
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R. Moore (1922)
Fundamenta Mathematicae
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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,...
Rudolph Hrycay (1970)
Fundamenta Mathematicae
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J. Hunt (1980)
Fundamenta Mathematicae
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Tzannes, V. (1998)
International Journal of Mathematics and Mathematical Sciences
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John Kline (1922)
Fundamenta Mathematicae
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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.