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Topologies generated by closed intervals.

Kurilić, Miloš S.; Pavlović, Aleksandar — 2005

Novi Sad Journal of Mathematics

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

Miloš S. Kurilić; Aleksandar Pavlović — 2014

Czechoslovak Mathematical Journal

We compare the forcing-related properties of a complete Boolean algebra $𝔹$ with the properties of the convergences $λ_{s}$ (the algebraic convergence) and $λ_{ls}$ on $𝔹$ generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that $λ_{ls}$ is a topological convergence iff forcing by $𝔹$ does not produce new reals and that $λ_{ls}$ is weakly topological if $𝔹$ satisfies condition $(ℏ)$ (implied by the $𝔱$ -cc). On the other hand, if $λ_{ls}$ is a weakly topological convergence, then $𝔹$ is a $2^{𝔥}$ -cc algebra...

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