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Universality of the μ-predictor

Christopher S. Hardin (2013)

Fundamenta Mathematicae

For suitable topological spaces X and Y, given a continuous function f:X → Y and a point x ∈ X, one can determine the value of f(x) from the values of f on a deleted neighborhood of x by taking the limit of f. If f is not required to be continuous, it is impossible to determine f(x) from this information (provided |Y| ≥ 2), but as the author and Alan Taylor showed in 2009, there is nevertheless a means of guessing f(x), called the μ-predictor, that will be correct except on a small set; specifically,...

Vietoris topology on spaces dominated by second countable ones

Carlos Islas, Daniel Jardon (2015)

Open Mathematics

For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets of a space...

ω ω -directedness and a question of E. Michael

Peg Daniels (1995)

Commentationes Mathematicae Universitatis Carolinae

We define ω ω -directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.

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