The Pointed Version of Lipscomb's Embedding Theorem

• Autores: Ivan Ivansic, Uros Milutinovic
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 1, 2005, págs. 173-192
• Idioma: inglés
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• Resumen

  • Let S(t) be the generalized Sierpinski curve, which is naturally identified with Lipscomb's space J(t).

    Then for any n-dimensional metric space X of weight t there is an embedding of X into Ln(t), where Ln(t) is the subset of S(t)n+1 of all points having at least one so called irrational coordinate. Here we prove 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, we prove a stronger result that the values of the embedding may be given in advance at any finite set of points of X.