We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version Esakia duality and system concrete isomorphisms equivalences. In way, we continue building tame topology, realising Grothendieck’s ideas. use up-spectral spaces define standard up-spectralification Kolmogorov space. This research gives more understanding definable over structures with top...

The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of prog...

Analogues of stepping–stone models are considered where the site– space is continuous, the migration process is a general Markov process, and the type–space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative represent...

Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representat...