What makes a Stone topological algebra Profinite

Stone duality, topological algebra, and recognition

Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...

Profinite Topological Spaces

It is well known [Hoc69, Joy71] that profinite T0-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space. (2) The T0-reflection of (X,τ) is a profinite T0-space. (3) (X,τ) is a quasi spectral space (in the sense of [BMM08]). (4) (X,τ) admits a ...

Polymeric Gas Separation Membranes: What Makes them Industrially more Attractive?

Compact Hausdorff Heyting algebras

We prove that the topology of a compact Hausdorff topological Heyting algebra is a Stone topology. It then follows from known results that a Heyting algebra is profinite iff it admits a compact Hausdorff topology that makes it a compact Hausdorff topological Heyting algebra.

What Makes a Revolution

Although property rights are the cornerstone of capitalist economies, throughout history existing claims have been frequently overturned and redefined by revolution. A fundamental question for economists is what makes revolutions more likely to occur. A large literature has found contradictory evidence for the effect of income and income inequality on revolt, possibly due to omitted variable bi...