The effective dimension spectrum of every polynomial curve contains at least two points, with the conjecture resolved for the subfamily of low-dimensional coefficient polynomials.
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Introduces constructive Φ-dimension, proves its point-to-set principle and Kolmogorov complexity characterization, and establishes equivalence of faithfulness conditions for Cantor coverings between Hausdorff and constructive levels.
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On the Constructive Dimension Spectrum of Polynomials
The effective dimension spectrum of every polynomial curve contains at least two points, with the conjecture resolved for the subfamily of low-dimensional coefficient polynomials.
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Point-to-set Principle and Constructive Dimension Faithfulness
Introduces constructive Φ-dimension, proves its point-to-set principle and Kolmogorov complexity characterization, and establishes equivalence of faithfulness conditions for Cantor coverings between Hausdorff and constructive levels.