Another application of the Effros theorem to the pseudo-arc
The absolute stability of a compact set is characterized in terms of a fundamental system of positive invariant neighborhoods.
MSC 2010: 54A25, 54A35.
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
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 with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...