The Pointed Version of Lipscomb's Embedding Theorem (CROSBI ID 117078)
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Ivanšić, Ivan ; Milutinović, Uroš
engleski
The Pointed Version of Lipscomb's Embedding Theorem
For a given weight of a spaces one identifies the generalized Sierpinski curve of this weight with the Lipscomb's 1- dimensional space and constructs a universal space for n- dimensional metric spaces of that weight. This universal space is a subset of the (n+1)-fold product of the generalized Sierpinski curve and consists of all points having at least one irrational coordinate. Here is proved that this embedding may be chosen in such a way that its value at a certain point (the base point) is given in advance. In fact, a stronger result is proved, namely, that the values of the embedding may be given in advance at any finite set of points.
generalized Sierpinski's curve; Lipscomb's space; universal space
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