engleski

A Universal separable metric space based on the triangular Sierpinski curve

Let \Sigma(3) be the triangular Sierpinski curve. Call the vertices of the triangles obtained during the construction of \Sigma(3) (with the exception of the first triangle) the rational points of \Sigma (3), and all other points the irrational points of \Sigma(3). Using results of Lipscomb and techniques and results of Milutinovi?, we prove that L_n(3)={x\in\Sigma(3)^(n+1): at least one coordinate of x is irrational} is a universal space for all metrizable spaces of dimension \leq n.

covering dimension; Sierpinski curve; universal space; Lipscomb's universal space; embedding; decompositions of toplogical spaces

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