On $D$-spaces and Discrete Families of Sets
| dc.creator | Dzamonja, Mirna | |
| dc.date | 2008-11-07 | |
| dc.date.accessioned | 2026-07-07T10:16:51Z | |
| dc.date.available | 2026-07-07T10:16:51Z | |
| dc.description | We prove several reflection theorems on $D$-spaces, which are Hausdorff topological spaces $X$ in which for every open neighbourhood assignment $U$ there is a closed discrete subspace $D$ such that \[ \bigcup\{U(x): x\in D\}=X. \] The upwards reflection theorems are obtained in the presence of a forcing axiom, while most of the downwards reflection results use large cardinal assumptions. The combinatorial content of arguments showing that a given space is a $D$-space, can be formulated using the concept of discrete families. We note the connection between non-reflection arguments involving discrete families and the well known question of the existence of families allowing partial transversals without having a transversal themselves, and use it to give non-trivial instances of the incompactness phenomenon in the context of discretisations. | |
| dc.description | and old paper, the previous version on arxiv only contained the latex macros | |
| dc.identifier | https://arxiv.org/abs/0811.1165 | |
| dc.identifier | http://arxiv.org/abs/0811.1165 | |
| dc.identifier | On $D$-spaces and Discrete Families of Sets, in AMS, DIMACS: Series in Discrete Mathematics and Theoretical Computer Sciences, ed. by S. Thomas 58 (2002), pg. 45-63 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173653 | |
| dc.subject | Logic | |
| dc.subject | 03E35, 54E20, 03E55 | |
| dc.title | On $D$-spaces and Discrete Families of Sets | |
| dc.type | text |