arXiv subjects

Servet Soyarslan

Publications and source records attributed to Servet Soyarslan.

3 recordsLinked to original sources

arXiv2025

Noetherian $π$-bases and Telgársky's Conjecture

We investigate Noetherian families and show that every topological space has a Noetherian $π$-base. We prove that if a topological space has some special Noetherian $π$-bases, then NONEMPTY has a 2-tactic in the Banach-Mazur game on a space $X$, denoted as $BM(X)$, whenever NONEMPTY has a winning strategy in BM(X). This result encompasses an important theorem of Galvin in this context and is related to Telgársky's conjecture on this subject. One of our examples is that any space $X$ with $πw(X)\leq ω_1$ has this special Noetherian $π$-base. We pose some questions about this topic.

math.GN↗

arXiv2022

A weakly Lindelöf space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$

We show that there exists a Tychono? weakly Lindelöf space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$. This result answers the following open questions. [2] Does a weakly Lindelöf space have the property $^*\mathcal{U}_{1}(\mathcal{O},\mathcal{O})$? [3] Is there a Tychono? 1-star-Lindelöf space which does not have the property $^*\mathcal{U}_{fin}(\mathcal{O},\mathcal{O})$?

math.GN↗

arXiv2021

A solution of a problem about Erdös Space

For Erdős space, $\mathfrak{E}$, let us define a topology, $τ_{clopen}$, which is generated by clopen subsets of $\mathfrak{E}$. A. V. Arhangel'skii and J. Van Mill asked whether the topology $τ_{clopen}$ is compatible with the group structure on $\mathfrak{E}$. In this paper, we give a negative answer for this question.

math.GN↗