Abstract Concept of Changeable Set

Coordinate transforms in kinematic changeable sets

“…In the papers [11,13] it is proved, that for any changeable set Z the following properties are performed: 2. For arbitrary l ∈ Lk (Z) and A ⊆ Bs(l) it is true the equality, l ← l A = A.…”

“…Assertion 2 ( [11,12]). Let l, m ∈ Lk (Z) be arbitrary areas of perception of any precisely visible changeable set Z.…”

“…In particular, mathematical apparatus of these papers allows only studying of universal coordinate transforms (that is coordinate transforms, which are uniquely determined by the geometrically-time position of the considered object). The present paper is based on the general theory of changeable sets [10][11][12][13]. In the paper the definitions of the actual and universal coordinate transform in kinematic changeable sets are presented.…”

“…In the present section we recall necessary denotations and concepts of the changeable sets theory, introduced in [11] (see also [10, 12-14, 16, 17]). Changeable and base changeable sets will be denoted by large calligraphy or Gothic letters.…”

“…Remark 3. From the definition of changeable set ( [13, Definition 3.1], [11,Definition 9.6]) it directly follows, that for any area of perception l ∈ Lk (Z) of any changeable set Z, Properties 1 and Properties 2 are holding, where we use all abbreviated variants of notations, described in the Remark 1 (but, with replacement of the symbol "B " by the symbol "l" and the term "base changeable set" by the term "area of perception").…”