Dynamic mereotopology III. Whiteheadean type of integrated point-free theories of space and time. II

This is the second part from the series of papers shortly denoted by part I [Algebra i Logika, 53, No. 3 (2014), 300–322] and part III [Algebra i Logika, 55, No. 3]. These papers are devoted to some Whiteheadean theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. The present part is devoted to the introduction of a point-based definition of dynamic model of space and standard dynamic contact algebra based on the so called snapshot construction. This model contains explicit time structure with explicit set of time points equipped with a before-after relation and a set of regions changing in time, called dynamic regions. The dynamic model of space contains several definable spatio-temporal relations between dynamic regions: space contact, time contact, precedence and some others. We prove for these relations some statements, which in part III are taken as axioms for the abstract definition of some natural classes of dynamic contact algebras, considered as algebraic formulation of dynamic mereotopology.