Andrea Pedrini

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In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space Rn with n > 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot detect topological dimension in the(More)
(See e.g. [6] for background.) When X is equipped with a distinguished basis D for its topology, closed under finite meets and joins, one can investigate situations where D is also closed under the implication (2), i.e., where D is a Heyting subalgebra of O (X). Recall that X is a spectral space if it is compact and T0, its collection D of compact open(More)
(See e.g. [6] for background.) When X is equipped with a distinguished basis D for its topology, closed under finite meets and joins, one can investigate situations where D is also closed under the implication (2), i.e., where D is a Heyting subalgebra of O (X). Recall that X is a spectral space if it is compact and T0, its collection D of compact open(More)
Neural gas (NG) is a robust vector quantization algorithm for which a descriptive mathematical model is known. According to this model, the output configuration produced by the NG algorithm samples the input data distribution with a density that follows a power law with a magnification factor that depends on data dimensionality only. The effects of shape in(More)
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