On the representation of changeable sets in the form of an automultiimage

Abstract

From an intuitive point of view, the multi-image construction procedure resembles the procedure of constructing the evolution scenario of some system in all possible reference frames, if we know its scenario of evolution in the given (fixed) reference frame. In the present paper it is investigated the problem of representation of a changeable set in the form of automultiimage that is in the form of the multi-image of some its reference frame. In particular we prove the necessary and sufficient condition for evolutionarily visible changeable set to be representable as automultiimage. Also using the last result we give the example of evolutionarily visible changeable set, which can not be represented as automultiimage.

Key words: Changeable sets, sixth Hilbert problem, evolution scenario, multi-image.

Full Text

Article Information

Title	On the representation of changeable sets in the form of an automultiimage
Source	Methods Funct. Anal. Topology, Vol. 31 (2025), no. 2, 82-105
DOI	10.31392/MFAT-npu26_2.2025.01
Milestones	Received 16/05/2025; Revised 22/07/2025
Copyright	The Author(s) 2025 (CC BY-SA)

Authors Information

Yaroslav I. Grushka
Institute of Mathematics NAS of Ukraine, Kyiv, Ukraine

Citation Example

Yaroslav I. Grushka, On the representation of changeable sets in the form of an automultiimage, Methods Funct. Anal. Topology 31 (2025), no. 2, 82-105.

BibTex

@article {MFAT2103,
    AUTHOR = {Yaroslav I. Grushka},
     TITLE = {On the representation of changeable sets in the form of an automultiimage},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {31},
      YEAR = {2025},
    NUMBER = {2},
     PAGES = {82-105},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_2.2025.01},
       URL = {https://mfat.imath.kiev.ua/article/?id=2103},
}

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