13 citations · 35 across the 19 of their papers we have counts for
21 papers
Countable compactness in powers of topological groups and Ramsey theoretic variations of compactness
Vinicius de Oliveira Rodrigues, Paul Jan Szeptycki, Artur Hideyuki Tomita
Countable compactness need not be preserved by finite products. Motivated by compactness notions for maps indexed by finite subsets of , we introduce cascade countable compactne…
A Wallace semigroup whose every finite power is countably compact
Juan Luis Jaisuño Fuentes-Maguiña, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We show that, assuming the existence of incomparable selective ultrafilters, there exists a Wallace semigroup whose infinite countable power is the least power which…
Remarks on SHD spaces and more divergence properties
Carlos David Jiménez-Flores, Alejandro Ríos-Herrejón, Alejandro Darío Rojas-Sánchez +2
The class of SHD spaces was recently introduced in [12]. The first part of this paper focuses on answering most of the questions presented in that article. For instance, we exhibit…
On powers of countably pracompact groups
Artur Hideyuki Tomita, Juliane Trianon-Fraga
In 1990, Comfort asked: is there, for every cardinal number , a topological group such that is countably compact for all cardinals , but $G^α…
Comfort's question on powers in and a Wallace semigroup whose cube is countably compact
J. L. J. Fuentes-Maguiña, A. H. Tomita
We prove that the existence of incomparable selective ultrafilters implies the existence of a Wallace semigroup whose cube is countably compact. In addition, assumin…
-compact group topologies without convergent sequences on countably cofinal torsion-free Abelian groups
Matheus Koveroff Bellini, Artur Hideyuki Tomita
We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group admits a Hausdorff group topology which is also $\mathcal{U…
Some pseudocompact-like properties in certain topological groups
Artur Hideyuki Tomita, Juliane Trianon-Fraga
We construct in ZFC a countably compact group without non-trivial convergent sequences of size , answering a question of Bellini, Rodrigues and Tomita. We also co…
Countably compact group topologies on arbitrarily large free Abelian groups
M. K. Bellini, K. P. Hart, V. O. Rodrigues +1
We prove that if there are incomparable selective ultrafilters then, for every infinite cardinal such that , there exists a group topology on the free Abel…
Forcing a classification of non-torsion Abelian groups of size at most with non-trivial convergent sequences
Matheus Koveroff Bellini, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We force a classification of all the Abelian groups of cardinality at most that admit a countably compact group with a non-trivial convergent sequence. In particula…
Maximal almost disjoint families and pseudocompactness of hyperspaces
Osvaldo Guzmán, Michael Hrušák, Vinicius de Oliveira Rodrigues +2
We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if holds. We further stu…
Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter
A. C. Boero, I. Castro-Pereira, A. H. Tomita
We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a conse…
A van Douwen-like ZFC theorem for small powers of countably compact groups without non-trivial convergent sequences
Artur Hideyuki Tomita
We show that if and there exists a group topology without non-trivial convergent sequences on an Abelian group such that is countably compact for each the…
Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters
M. K. Bellini, A. C. Boero, V. O. Rodrigues +1
Assuming the existence of incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality that admit a countably compact…
On -compact group topologies on direct sums of
Matheus Koveroff Bellini, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
We prove that if is a selective ultrafilter then has a -compact group topology without non-trivial convergent sequences, for each infinite cardinal $κ=κ^…
Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences
{Matheus Koveroff Bellini, Ana Carolina Boero, Irene Castro Pereira +2
Under , we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality , by showing that if a non-torsion Abelian group of size…
Small MAD families whose Isbell-Mrówka spaces are pseudocompact
Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita
Given a countable transitive model for ZFC+CH, we prove that one can produce a maximal almost disjoint family in whose Vietoris Hyperspace of its Isbell-Mrówka space is pse…
Small Cardinals and the Pseudocompactness of Hyperspaces of Subspaces of
Y. F. Ortiz-Castillo, V. O. Rodrigues, A. H. Tomita
We study the relations between a generalization of pseudocompactness, named -pseudocompactness, the countably compactness of subspaces of and the pseudocompactness of…
Finite powers of selectively pseudocompact groups
S. Garcia-Ferreira, A. H. Tomita
A space is called {\it selectively pseudocompact} if for each sequence of pairwise disjoint nonempty open subsets of there is a sequence $(x_{n}…
-Ideals and outer measures on the real line
S. García-Ferreira, A. H. Tomita, Y. F. Ortiz-Castillo
A {\it weak selection} on is a function such that for each . In this article, w…
On topological groups admitting a base at identity indexed with
Arkady G. Leiderman, Vladimir G. Pestov, Artur H. Tomita
A topological group is said to have a local -base if the neighbourhood system at identity admits a monotone cofinal map from the directed set . In particular, every m…
Bornoligies, Topological Games and Function Spaces
Jiling Cao, Artur H. Tomita
In this paper, we continue the study of function spaces equipped with topologies of (strong) uniform convergence on bornologies initiated by Beer and Levi \cite{beer-levi:09}. In p…