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Another note on countable Boolean algebras

Lutz Heindorf (1996)

Commentationes Mathematicae Universitatis Carolinae

We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.

Aposyndesis in

José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2023)

Commentationes Mathematicae Universitatis Carolinae

We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions P ( a , b ) with the property that every prime number that divides a also divides b , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...

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