Artur Hideyuki Tomita
University of São Paulo
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Featured researches published by Artur Hideyuki Tomita.
Proceedings of the American Mathematical Society | 2005
S. Garcia-Ferreira; Artur Hideyuki Tomita; Stephen Watson
We prove that the existence of a selective ultrafilter on ω implies the existence of a countably compact group without non-trivial convergent sequences all of whose powers are countably compact. Hence, by using a selective ultrafilter on ω, it is possible to construct two countably compact groups without non-trivial convergent sequences whose product is not countably cornpact.
Topology and its Applications | 1999
Artur Hideyuki Tomita
Abstract We show under MAcountable the existence of a countable subgroup E of 2 c such that the group H generated by E and G = {x ϵ 2 c } : supp x is bounded in c is a group as in the title. We also show under MAcountable that for each k ϵ N there exists a countable family {{E n : n ϵ N }} of countable subgroups of 2 c such that if Hn = En + G, then for each subset F of N of size k, ΠnϵFHn is incountable compact, while for each subset F of N of size k + 1, ΠnϵFHn is not countably compact.
Topology and its Applications | 2002
S. Garcia-Ferreira; Valentin Gutev; Tsugunori Nogura; Manuel Sanchis; Artur Hideyuki Tomita
Abstract We study properties of Hausdorff spaces X which depend on the variety of continuous selections for their Vietoris hyperspaces F (X) of closed non-empty subsets. Involving extreme selections for F (X) , we characterize several classes of connected-like spaces. In the same way, we also characterize several classes of disconnected-like spaces, for instance all countable scattered metrizable spaces. Further, involving another type of selections for F (X) , we study local properties of X related to orderability. In particular, we characterize some classes of orderable spaces with only one non-isolated point.
Proceedings of the American Mathematical Society | 2003
Artur Hideyuki Tomita
E. K. van Douwen asked in 1980 whether the cardinality of a countably compact group must have uncountable cofinality in ZFC. He had shown that this was true under GCH. We answer his question in the negative. V. I. Malykhin and L. B. Shapiro showed in 1985 that under GCH the weight of a pseudocompact group without non-trivial convergent sequences cannot have countable cofinality and showed that there is a forcing model in which there exists a pseudocompact group without non-trivial convergent sequences whose weight is w 1 < c. We show that it is consistent that there exists a countably compact group without non-trivial convergent sequences whose weight is N w .
Publicacions Matematiques | 2007
Valentin Gutev; Artur Hideyuki Tomita
Every (continuous) selection for the non-empty 2-point subsets of a space
Proceedings of the American Mathematical Society | 2007
Jiling Cao; Artur Hideyuki Tomita
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Topology and its Applications | 1999
Artur Hideyuki Tomita
naturally defines an interval-like topology on
Topology and its Applications | 2018
Y.F. Ortiz-Castillo; V.O. Rodrigues; Artur Hideyuki Tomita
X
Archive | 2000
Piotr B. Koszmider; Artur Hideyuki Tomita; Stephen Watson
. In the present paper, we demonstrate that, for a second-countable zero-dimensional space
Commentationes Mathematicae Universitatis Carolinae | 1996
Artur Hideyuki Tomita
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