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In these notes we introduce and investigate two new games called R-nw-selective game and the M-nw-selective game. These games naturally arise from the corresponding selection principles involving networks introduced in \cite{BG}.
Externí odkaz:
http://arxiv.org/abs/2312.12052
Publikováno v:
In Topology and its Applications 15 June 2024 351
Autor:
Aurichi, Leandro F., Duzi, Matheus
We present a new variation of the classical selection principles $\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$ ($k\in\mathbb N$) and $\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$ that formally lies between these two properties. As in the case o
Externí odkaz:
http://arxiv.org/abs/1901.09371
Autor:
Aurichi, Leandro F., Bella, Angelo
The main goal of the paper is the full proof of a cardinal inequality for a space with points $G_\delta $, obtained with the help of a long version of the Menger game. This result, which improves a similar one of Scheepers and Tall, was already estab
Externí odkaz:
http://arxiv.org/abs/1711.03217
We present an internal characterization for the productively Lindel\"of property, thus answering a long-standing problem attributed to Tamano. We also present some results about the relation Alster spaces vs. productively Lindel\"of spaces.
Externí odkaz:
http://arxiv.org/abs/1704.03843
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For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then the second
Externí odkaz:
http://arxiv.org/abs/1603.09715
Autor:
Aurichi, Leandro F., Lara, Dione A.
We present a selection principle $S_1(\mathcal{O},\mathcal{H})$ that characterizes the $G_{\delta}$-diagonal property. We also present a topological game induced by this selection principle and we study the relations between this game and the $G_{\de
Externí odkaz:
http://arxiv.org/abs/1602.07002
Autor:
Aurichi, Leandro F., Duzi, Matheus
Publikováno v:
In Topology and its Applications 15 March 2021 291
Autor:
Aurichi, Leandro F., Bella, Angelo
We try to characterize those Tychonoff spaces $X$ such that $\beta X \setminus X$ has the Menger property.
Externí odkaz:
http://arxiv.org/abs/1407.7495