Olena Hryniv: A parallel metrization theorem
27/11/19 21:51
Tuesday, December 3, 2019 17:15
Room: D1-215
Speaker: Olena Hryniv, Ivan Franko National University of Lviv
Title: A parallel metrization theorem
Abstract. Two non-empty sets \(A, B\) of a metric space \( (X , d)\) are called parallel if \( d(a, B) = d(A, B) = d(A, b) \) for any points \( a \in A \) and \( b \in B.\) Answering a question posed on mathoverflow.net, we prove that for a cover \( \mathcal{C}\) of a metrizable space \(X\) by compact subsets, the following conditions are equivalent:
(i) the topology of \(X\) is generated by a metric d such that any two sets \(A, B\) of \(\mathcal{C}\) are parallel;
(ii) the cover \( \mathcal{C}\) is disjoint, lower semicontinuous and upper semicontinuous.
Room: D1-215
Speaker: Olena Hryniv, Ivan Franko National University of Lviv
Title: A parallel metrization theorem
Abstract. Two non-empty sets \(A, B\) of a metric space \( (X , d)\) are called parallel if \( d(a, B) = d(A, B) = d(A, b) \) for any points \( a \in A \) and \( b \in B.\) Answering a question posed on mathoverflow.net, we prove that for a cover \( \mathcal{C}\) of a metrizable space \(X\) by compact subsets, the following conditions are equivalent:
(i) the topology of \(X\) is generated by a metric d such that any two sets \(A, B\) of \(\mathcal{C}\) are parallel;
(ii) the cover \( \mathcal{C}\) is disjoint, lower semicontinuous and upper semicontinuous.