Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Spadaro, Santi"'
In this paper we investigate R-,H-, and M-{\it nw}-selective properties introduced in \cite{BG}. In particular, we provide consistent uncountable examples of such spaces and we define \textit{trivial} R-,H-, and M-{\it nw}-selective spaces the ones w
Externí odkaz:
http://arxiv.org/abs/2407.18713
The cellular-Lindel\"of property is a common generalization of the Lindel\"of property and the countable chain condition that was introduced by Bella and Spadaro in 2018. We solve two questions of Alas, Gutierrez-Dominguez and Wilson by constructing
Externí odkaz:
http://arxiv.org/abs/2406.14509
Autor:
Bella, Angelo, Spadaro, Santi
Publikováno v:
Topology Proceedings 59 (2022), 89--98
We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindel\"of. After distinguishing this property from the Lindel\"of property we make various remarks about cardinal invariants of SDL spa
Externí odkaz:
http://arxiv.org/abs/2404.00455
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), 3177--3187
We characterize when the countable power of a Corson compactum has a dense metrizable subspace and construct consistent examples of Corson compacta whose countable power does not have a dense metrizable subspace. We also give several remarks about cc
Externí odkaz:
http://arxiv.org/abs/2403.15799
A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponentially separability. We start by studying these properties in GO spaces, where we extend results
Externí odkaz:
http://arxiv.org/abs/2403.15552
Autor:
Spadaro, Santi, Szeptycki, Paul
Publikováno v:
Acta Mathematica Hungarica 166 (2022), pp. 92--96
We construct a consistent example of a topological space $Y=X \cup \{\infty\}$ such that: 1) $Y$ is regular. 2) Every $G_\delta$ subset of $Y$ is open. 3) The point $\infty$ is not isolated, but it is not in the closure of any discrete subset of $X$.
Externí odkaz:
http://arxiv.org/abs/2403.01880
Autor:
Bella, Angelo, Spadaro, Santi
A topological space $X$ is selectively highly divergent (SHD) if for every sequence of non-empty open subsets $\{U_n: n\in \omega \}$ of $X$, we can pick a point $x_n\in U_n$, for every $n<\omega$, such that the sequence $\{x_n: n\in\omega\} $ has no
Externí odkaz:
http://arxiv.org/abs/2309.11954
Autor:
Spadaro, Santi
Let $F(X)$ be the supremum of cardinalities of free sequences in $X$. We prove that the radial character of every Lindel\"of Hausdorff almost radial space $X$ and the set-tightness of every Lindel\"of Hausdorff space are always bounded above by $F(X)
Externí odkaz:
http://arxiv.org/abs/1912.12706
Autor:
Bella, Angelo, Spadaro, Santi
We prove that if $X$ is a regular space with no uncountable free sequences, then the tightness of its $G_\delta$ topology is at most continuum and if $X$ is in addition Lindel\"of then its $G_\delta$ topology contains no free sequences of length larg
Externí odkaz:
http://arxiv.org/abs/1911.11461
Autor:
Bella, Angelo, Spadaro, Santi
We present a bound for the weak Lindel\"of number of the $G_\delta$-modification of a Hausdorff space which implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology:
Externí odkaz:
http://arxiv.org/abs/1907.04344