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http://hdl.handle.net/11320/21428Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Grabowski, Adam | - |
| dc.date.accessioned | 2026-11-04T13:46:21Z | - |
| dc.date.available | 2026-11-04T13:46:21Z | - |
| dc.date.issued | 2005 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 13, Issue 1, Pages 139-146 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/21428 | - |
| dc.description.abstract | This is the first Mizar article in a series aiming at a complete formalization of the textbook “General Topology” by Engelking [7]. We cover the first part of Section 1.3, by defining such notions as a derivative of a subset A of a topological space (usually denoted by Ad, but Der A in our notation), the derivative and the boundary of families of subsets, points of accumulation and isolated points. We also introduce dense-in-itself, perfect and scattered topological spaces and formulate the notion of the density of a space. Some basic properties are given as well as selected exercises from [7]. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | CC BY-SA 4.0 | - |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | - |
| dc.title | On the Boundary and Derivative of a Set | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2005 University of Białystok | pl |
| dc.rights.holder | This work is licensed under the Creative Commons License. | pl |
| dc.description.Affiliation | University of Białystok | pl |
| dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990. | pl |
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| dc.description.references | Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. | pl |
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| dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. | pl |
| dc.description.references | Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231–237, 1990. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 13 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 139 | pl |
| dc.description.lastpage | 146 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2005, Volume 13, Issue 1 | |
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