Zobrazeno 1 - 10
of 202
pro vyhledávání: '"Rodrigues, Vinícius P."'
We show that, assuming the existence of $\mathfrak{c}$ incomparable selective ultrafilters, there exists a Wallace semigroup whose infinite countable power is the least power which fails to be countably compact. This answers positively Question 9.4 o
Externí odkaz:
http://arxiv.org/abs/2403.00205
We prove the consistency of the existence of a $Q$-set whose square is not a $\Delta$-set and that if there is a $\Delta$-set, then there exists a $\Delta$-set whose all finite powers are $\Delta$-sets.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2312.13973
We show that both $\mathfrak{ap=c}$ and $\diamondsuit(\mathfrak{b})$ imply the existence of MAD families with pseudocompact Vietoris hyperspace, substantially expanding the list of models where their existence is known. We also discuss some propertie
Externí odkaz:
http://arxiv.org/abs/2309.03405
We introduce a new class of almost disjoint families which we call fin-intersecting almost disjoint families. They are related to almost disjoint families whose Vietoris Hyperspace of their Isbell-Mr\'owka spaces are pseudocompact. We show that under
Externí odkaz:
http://arxiv.org/abs/2212.01484
We recall some classical results relating normality and some natural weakenings of normality in $\Psi$-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$-sets, $\lambda$-sets and $\sigma$-sets. We in
Externí odkaz:
http://arxiv.org/abs/2112.09830
We explore almost-normality in Isbell-Mr\'owka spaces and some related concepts. We use forcing to provide an example of an almost-normal not normal almost disjoint family, explore the concept of semi-normality in Isbell-Mr\'owka spaces, define the c
Externí odkaz:
http://arxiv.org/abs/2009.10209
We force a classification of all the Abelian groups of cardinality at most $2^\mathfrak c$ that admit a countably compact group with a non-trivial convergent sequence. In particular, we answer (consistently) Question 24 of Dikranjan and Shakhmatov fo
Externí odkaz:
http://arxiv.org/abs/2006.09961
Autor:
Guzmán, Osvaldo, Hrušák, Michael, Rodrigues, Vinicius de Oliveira, Todorčević, Stevo, Tomita, Artur Hideyuki
We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if $\mathsf{MA}_\mathfrak c (\mathcal P(\omega)/\mathrm{fin})$ holds. We further study the question whether there is a maximal almost disjoint family
Externí odkaz:
http://arxiv.org/abs/2004.08760
We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first arbitrari
Externí odkaz:
http://arxiv.org/abs/1904.05928
Autor:
Bellini, {Matheus Koveroff, Boero, Ana Carolina, Pereira, Irene Castro, Rodrigues, Vinicius de Oliveira, Tomita, Artur Hideyuki
Under $\mathfrak{p} = \mathfrak{c}$, we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality ${\mathfrak c}$ , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it
Externí odkaz:
http://arxiv.org/abs/1810.05140