Spaces with increment of dimension n
M. Charalambous (1976)
Fundamenta Mathematicae
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M. Charalambous (1976)
Fundamenta Mathematicae
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Alois Švec (1968)
Czechoslovak Mathematical Journal
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Roman Sikorski (1951)
Fundamenta Mathematicae
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Miroslav Katětov (1995)
Commentationes Mathematicae Universitatis Carolinae
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Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.
Enrico Carlini, Maria Catalisano, Anthony Geramita (2011)
Open Mathematics
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R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).