Pointwise density topology
| Autor: | Górajska Magdalena |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Open Mathematics, Vol 13, Iss 1 (2015) |
| Druh dokumentu: | article |
| ISSN: | 2391-5455 2015-0008 |
| DOI: | 10.1515/math-2015-0008 |
| Popis: | The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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