November 2019
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.
Robert Rałowski: Mycielski among trees - nonstandard proofs, part 2
04/11/19 17:11
Tuesday, November 5, 2019 17:15
Room: D1-215
Speaker: Robert Rałowski
Title: Mycielski among trees - nonstandard proofs, part 2
Abstract. We present proofs of Mycielski like Theorem for sigma ideal of meager subsets of Baire space and Egglestone like Theorem. In both proofs we use Schoenfield Absolutness Theorem. In Mycielski Theorem we replace the term perfect set by slalom perfect set what is some strengthen of the classical version. Results are from common paper with Marcin Michalski and Szymon Żeberski.
Room: D1-215
Speaker: Robert Rałowski
Title: Mycielski among trees - nonstandard proofs, part 2
Abstract. We present proofs of Mycielski like Theorem for sigma ideal of meager subsets of Baire space and Egglestone like Theorem. In both proofs we use Schoenfield Absolutness Theorem. In Mycielski Theorem we replace the term perfect set by slalom perfect set what is some strengthen of the classical version. Results are from common paper with Marcin Michalski and Szymon Żeberski.