a ~A de Vries algebra is a pair consisting of a complete Boolean algebra (B, 4) with the relation 4 (precedes) and a binary relation X (strictly precedes) for which: This idea leads to the following definition :Дefinition 3. In general, a de Vries algebra is defined as a Boolean algebra with an additional relation X that satisfies the same properties as the algebra RX. One can check that the class RX with the relation 4 is a complete Boolean algebra, with negation -A = Int(X - A). On 7ZX, we can define A =4 B ^ A C B and A - A c B. The original example of such an object is the class 1ZX of all regular open subsets of a compact Hausdorff space X, i.e., open subsets A for which the interior Int (A) of the closure A coincides with the original set A. In mathematics, there is another case when we have a set with two orders: the case of so-called de Vries algebras. de Vries Algebras and their Relation to Kinematic SpacesДe Vries algebras. A 1-1 mapping t : X ^ X of a kinematic space onto itself is called a T-transformation if t(t(a)) = a for all a and a 4 b ^ t(b) 4 t(a).Дў. Thus, we arrive at the following definition.Дefinition 2. Another property is that T-transformation reverses the order of causality. One important property of this transformation is that if we apply it twice, we get the same point back. In particular, an important symmetry is T-transformation, a symmetry with respect to reversal of time t ^ -t. The notion of symmetry is very important in modern physics, to the extent that, starting with the quarks, physical theories are usually formulated in terms of symmetries - and not in terms of differential equations as in the past see, e.g. Similarly, if I rotate myself 90 degrees and drop the ball again, I will get the same trajectory but rotated by 90 degrees. to be more precise, obtained by shift from the previous one. It is reasonable to expect that the ball will fall, and that its trajectory will be the same as before I can then shift my position, and drop the ball again. For example, suppose that I dropped the ball, then it fall down.

In mathematical terms, similarity corresponds to symmetry, and similarity of outcomes - to invariance. The main basis for prediction is that we have observed similar situations in the past, and thus we expect similar outcomes as in those past situations. Main objectives of science is prediction. Symmetry: a fundamental property of the physical world. It has been proven that a X b ^ c or a ^ b X c imply a X c. To describe such situations, in the 1960s, geometers H.

In all these situations, what remains is causality -an ordering relation. However, in several physically interesting situations smoothness is violated: near the Big Bang, at the black holes, and on the microlevel, when we take into account quantum effects. Traditionally, in physics, space-times are described by (pseudo-)Riemann spaces, i.e., by smooth manifolds with a tensor metric field. Kinematic Spaces and de Vries Algebras: Towards Possible Physical Meaning of de Vries Algebras

Speed of causality