Isaac Gorelic

Learn More
We define a compactum X to be AB-compact if the cofinality of the character χ(x, Y ) is countable whenever x ∈ Y and Y ⊂ X. It is a natural open question if every AB-compactum is necessarily first countable. We strengthen several results from [Arhangel’skii and Buzyakova, Convergence in compacta and linear Lindelöfness, CMUC 39 (1998), no. 1, 159–166] by(More)
We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space X whose square X is again Lindelöf but its cube X has a closed discrete subspace of size c, hence the Lindelöf degree L(X) = c. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space X such that L(X) = א0 for all(More)
A topological space X is called weakly first countable, if for every point x there is a countable family {Cx n | n ∈ ω} such that x ∈ C n+1 ⊆ C n and such that U ⊂ X is open iff for each x ∈ U some C n is contained in U . This weakening of first countability is due to A. V. Arhangelskii from 1966, who asked whether compact weakly first countable spaces are(More)
We define a compactum X to be AB-compact if the cofinality of the character χ(x, Y ) is countable whenever x ∈ Y and Y ⊂ X. It is a natural open question if every AB-compactum is necessarily first countable. We strengthen several results from [Arhangel’skii and Buzyakova, Convergence in compacta and linear Lindelöfness, Comment. Math. Univ. Carolin. 39(More)
  • 1