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Publications (25)

math.GN2017

Cardinal Invariants for the $G_{I^} ´$ topology

Angelo Bella, Santi Spadaro

We prove upper bounds for the spread, the LindelÃ¶f number and the weak LindelÃ¶f number of the $G_{I^} ´$ -topology on a topological space and apply a few of our bounds to give a short…

math.GN2017

On the cardinality of almost discretely Lindelof spaces

Angelo Bella, Santi Spadaro

A space is said to be "almost discretely LindelÃ¶f" if every discrete subset can be covered by a LindelÃ¶f subspace. JuhÃ¡sz, Tkachuk and Wilson asked whether every almost discrete…

math.GN2016

On cardinality bounds involving the weak LindelÃ¶f degree

Angelo Bella, Nathan Carlson

We give a general closing-off argument in Theorem 2.1 from which several corollaries follow, including (1) if $X$ is a locally compact Hausdorff space then $∣ X ∣ \leq 2^{w L (X) I ¨ (X)}$ …

math.GN2010

P-spaces and the Whyburn property

Angelo Bella, Camillo Costantini, Santi Spadaro

We investigate the Whyburn and weakly Whyburn property in the class of $P$ -spaces, that is spaces where every countable intersection of open sets is open. We construct examples of…

math.GN2019

On weakening tightness to weak tightness

Angelo Bella, Nathan Carlson

The weak tightness $w t (X)$ of a space $X$ was introduced in [11] with the property $w t (X) \leq t (X)$ . We investigate several well-known results concerning $t (X)$ and consider whethe…

math.GN2019

Pseudoradial spaces and copies of $I ¨ _{1} + 1$

Angelo Bella, Alan Dow, Rodrigo HernÃ¡ndez-GutiÃ©rrez

In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfr…

math.GN2021

More on Cardinality Bounds Involving the Weak LindelÃ¶f degree

Angelo Bella, Nathan Carlson, Ivan Gotchev

We give several new bounds for the cardinality of a Hausdorff topological space $X$ involving the weak LindelÃ¶f degree $w L (X)$ . In particular, we show that if $X$ is extremally di…

math.GN2017

A definitive improvement of a game-theoretic bound and the long tightness game

Leandro F. Aurichi, Angelo Bella

The main goal of the paper is the full proof of a cardinal inequality for a space with points $G_{I^} ´$ , obtained with the help of a long version of the Menger game. This result, whic…

math.GN2023

On two questions on selectively highly divergent spaces

Angelo Bella, Santi Spadaro

A topological space $X$ is selectively highly divergent (SHD) if for every sequence of non-empty open subsets ${U_{n} : n \in I ¨ }$ of $X$ , we can pick a point $x_{n} \in U_{n}$ , for every…

math.GN2018

A note on rank 2 diagonals

Angelo Bella, Santi Spadaro

We solve two questions regarding spaces with a ( $G_{I^} ´$ )-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos regarding weakly LindelÃ¶f spaces with a $G_{I^} ´$ -diagona…

math.GN2016

Selective game versions of countable tightness with bounded finite selections

Leandro F. Aurichi, Angelo Bella, Rodrigo R. Dias

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 I ¨ $ , the first pl…

math.GN2024

Strongly discrete subsets with LindelÃ¶f closures

Angelo Bella, Santi Spadaro

We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is LindelÃ¶f. After distinguishing this property from the LindelÃ¶f p…

math.GN2019

On Cellular-Compact and related spaces

Angelo Bella

Tkachuk and Wilson proved that a regular first countable cellular-compact space has cardinality not exceeding the continuum. In the same paper they asked if this result continues t…

math.GN2014

On a game theoretic cardinality bound

Leandro F. Aurichi, Angelo Bella

The main purpose of the paper is the proof of a cardinal inequality for a space with points $G_{I^} ´$ , obtained with the help of a long version of the Menger game. This result improve…

math.GN2014

Topological games and productively countably tight spaces

Leandro F. Aurichi, Angelo Bella

The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game $\gone(Î©_x, Î©_x)$ for every $x \in X$ , then $X$ is p…

math.GN2019

A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality

Angelo Bella, Santi Spadaro

We present a bound for the weak LindelÃ¶f number of the $G_{I^} ´$ -modification of a Hausdorff space which implies various known cardinal inequalities, including the following two fund…

math.GN2013

Infinite games and cardinal properties of topological spaces

Angelo Bella, Santi Spadaro

Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an…

math.GN2011

Variations of selective separability II: discrete sets and the influence of convergence and maximality

Angelo Bella, Mikhail Matveev, Santi Spadaro

A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_{n} : n \in I ¨ )$ one can pick finite (respectively, one-point) subsets $F_n\subset…

math.GN2019

Cardinal invariants of cellular-Lindelof spaces

Angelo Bella, Santi Spadaro

A space $X$ is said to be "cellular-LindelÃ¶f" if for every cellular family $U$ there is a LindelÃ¶f subspace $L$ of $X$ which meets every element of $U$ . Cellu…

math.GN2016

Menger remainders of topological groups

Angelo Bella, SeÃ§il TokgÃ¶z, Lyubomyr Zdomskyy

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we s…

math.GN2014

When is a space Menger at infinity?

Leandro F. Aurichi, Angelo Bella

We try to characterize those Tychonoff spaces $X$ such that $I^^{2} X ∖ X$ has the Menger property.

math.GN2012

Some observations on compact indestructible spaces

Angelo Bella

Inspired by a recent work of Dias and Tall, we show that a compact indestructible space is sequentially compact. We also prove that a Lindelof Hausdorff indestructible space has th…

math.GN2020

A common extension of LindelÃ¶f, H-closed and ccc

Angelo Bella

The inequality $∣ X ∣ \leq 2^{I ¨ (X)}$ has been proved to be true for LindelÃ¶f spaces (Arhangel'ski\uÄ±, 1969), $H$ -closed spaces (Dow-Porter, 1982) and ccc spaces (Hajnal-JuÃ¡sz 196…

math.GN2018

A non-discrete space $X$ with $C_{p} (X)$ Menger at infinity

In a paper by Bella, TokgÃ¶s and Zdomskyy it is asked whether there exists a Tychonoff space $X$ such that the remainder of $C_{p} (X)$ in some compactification is Menger but not $I ¨ $ …

math.GN2020

Upper bounds for the tightness of the $G_{I^} ´$ -topology

Angelo Bella, Santi Spadaro

We prove that if $X$ is a regular space with no uncountable free sequences, then the tightness of its $G_{I^} ´$ topology is at most continuum and if $X$ is in addition LindelÃ¶f then…

Publications (25)

Cardinal Invariants for the GI^​´ topology

On the cardinality of almost discretely Lindelof spaces

On cardinality bounds involving the weak LindelÃ¶f degree

P-spaces and the Whyburn property

On weakening tightness to weak tightness

Pseudoradial spaces and copies of I¨1​+1

More on Cardinality Bounds Involving the Weak LindelÃ¶f degree

A definitive improvement of a game-theoretic bound and the long tightness game

On two questions on selectively highly divergent spaces

A note on rank 2 diagonals

Selective game versions of countable tightness with bounded finite selections

Strongly discrete subsets with LindelÃ¶f closures

On Cellular-Compact and related spaces

On a game theoretic cardinality bound

Topological games and productively countably tight spaces

A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality

Infinite games and cardinal properties of topological spaces

Variations of selective separability II: discrete sets and the influence of convergence and maximality

Cardinal invariants of cellular-Lindelof spaces

Menger remainders of topological groups

When is a space Menger at infinity?

Some observations on compact indestructible spaces

A common extension of LindelÃ¶f, H-closed and ccc

A non-discrete space X with Cp​(X) Menger at infinity

Upper bounds for the tightness of the GI^​´-topology

Cardinal Invariants for the $G_{I^} ´$ topology

Pseudoradial spaces and copies of $I ¨ _{1} + 1$

A non-discrete space $X$ with $C_{p} (X)$ Menger at infinity

Upper bounds for the tightness of the $G_{I^} ´$ -topology