Bibliographic Details
| Title: |
On the tightness of $G_\delta$-modifications |
| Authors: |
Dow, Alan, Juhász, István, Soukup, Lajos, Szentmiklóssy, Zoltán, Weiss, William |
| Publication Year: |
2018 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - General Topology, 54A25, 03E35, 54A35 |
| More Details: |
The $G_\delta$-modification $X_\delta$ of a topological space $X$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all $G_\delta$ subsets of $X$. Bella and Spadaro recently investigated the connection between the values of various cardinal functions taken on $X$ and $X_\delta$, respectively. In their paper, as Question 2, they raised the following problem: Is $t(X_\delta) \le 2^{t(X)}$ true for every (compact) $T_2$ space $X$? Note that this is actually two questions. In this note we answer both questions: In the compact case affirmatively and in the non-compact case negatively. In fact, in the latter case we even show that it is consistent with ZFC that no upper bound exists for the tightness of the $G_\delta$-modifications of countably tight, even Frechet spaces.
Comment: 9 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/1805.02228 |
| Accession Number: |
edsarx.1805.02228 |
| Database: |
arXiv |
