On selective absolute star-Lindelöfness Bonanzinga, Maddalena; Cuzzupé, Maria Vittoria; Sakai, Masami
Topology and its applications,
04/2017, Letnik:
221
Journal Article
Recenzirano
Odprti dostop
A space X is selectively absolutely star-Lindelöf if for any open cover U of X and any sequence (Dn:n∈ω) of dense subsets of X, there are finite sets Fn⊂Dn (n∈ω) such that St(⋃n∈ωFn,U)=X. This notion ...was introduced by S. Bhowmik 3, and it lies between absolute countable compactness in Matveev 9 and absolute star-Lindelöfness in Bonanzinga 4. In this paper, we distinguish absolute star-Lindelöfness from selective absolute star-Lindelöfness, and study the general properties of selectively absolutely star-Lindelöf spaces.
We consider combinatorial versions of classical separation axioms, give various examples of spaces satisfying them, consider interrelations between them and also how classical results including ...separation axioms extend to these new notions. We also consider their role in restricting cardinality of topological spaces and pose several open problems.
Diagonalizations of dense families Bonanzinga, Maddalena; Cammaroto, Filippo; Pansera, Bruno Antonio ...
Topology and its applications,
03/2014, Letnik:
165
Journal Article
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Odprti dostop
We develop a unified framework for the study of classic and new properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. ...Our classification draws upon a large number of methods and constructions scattered in the literature, and on several novel results concerning the classic properties.
Projective versions of selection principles Bonanzinga, Maddalena; Cammaroto, Filippo; Matveev, Mikhail
Topology and its applications,
04/2010, Letnik:
157, Številka:
5
Journal Article
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All spaces are assumed to be Tychonoff. A space
X is called projectively
P
(where
P
is a topological property) if every continuous second countable image of
X is
P
. Characterizations of projectively ...Menger spaces
X in terms of continuous mappings
f
:
X
→
R
ω
, of Menger base property with respect to separable pseudometrics and a selection principle restricted to countable covers by cozero sets are given. If all finite powers of
X are projectively Menger, then all countable subspaces of
C
p
(
X
)
have countable fan tightness. The class of projectively Menger spaces contains all Menger spaces as well as all
σ-pseudocompact spaces, and all spaces of cardinality less than
d
. Projective versions of Hurewicz, Rothberger and other selection principles satisfy properties similar to the properties of projectively Menger spaces, as well as some specific properties. Thus,
X is projectively Hurewicz iff
C
p
(
X
)
has the Monotonic Sequence Selection Property in the sense of Scheepers;
βX is Rothberger iff
X is pseudocompact and projectively Rothberger. Embeddability of the countable fan space
V
ω
into
C
p
(
X
)
or
C
p
(
X
,
2
)
is characterized in terms of projective properties of
X.
A class of posets, called thin posets, is introduced, and it is shown that every thin poset can be covered by a finite family of trees. This fact is used to show that (within ZFC) every separable ...monotonically Menger space is first countable. This contrasts with the previously known fact that under CH there are countable monotonically Lindelöf spaces which are not first countable.
On the Urysohn number of a topological space Bonanzinga, Maddalena; Cammaroto, Filippo; Matveev, Mikhail
Quaestiones mathematicae,
12/2011, Letnik:
34, Številka:
4
Journal Article
Recenzirano
The Urysohn number of a space X is U(X) = min{τ: for every subset A ⊂ X such that |A| ≥ τ one can pick neighborhoods U
a
∋ a for all a ∈ A so that
Some known statements about Urysohn spaces can be ...generalized in terms of the Urysohn number.
Monotone partitions and almost partitions Bonanzinga, Maddalena; Cammaroto, Filippo; van Mill, Jan ...
Topology and its applications,
12/2014, Letnik:
178
Journal Article
Recenzirano
Odprti dostop
In this paper we are interested in monotone versions of partitionability of topological spaces and weak versions thereof. We identify several classes of spaces with these properties by constructing ...trees of open sets with various properties.
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}.
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