The topology of perceptive functions as a corollary of the theorem of existence in closed spaces

Bounias, M.; Bonaly, A.

doi:10.1016/s0303-2647(97)01706-1

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…In the absence of "given" knowledge of what an object could be, Krasnoholovets (1997Krasnoholovets ( , 2000aKrasnoholovets ( , 2001a and Krasnoholovets and Byckov (2000) and Krasnoholovets and Ivanovsky (1993), proposed that a corpuscle could be represented by a local change in the geometry of a lattice. Independently, Bounias and Bonaly (1995, 1997a studied why could a mathematical space exist and how could it provide existence to a physical-like space. It was found that the results support both the hypothesis of existence of a founding lattice of Krasnoholovets et al, and the prediction of emergence of the phenomenon of self-conscious perception, which could stand for a major characteristic of life (Bounias, 2000a, b;Bounias and Bonaly, 1997b).…”

Section: Predictions Of Fundamental Physical Parametersmentioning

confidence: 99%

Scanning the structure of ill‐known spaces: Part 2. Principles of construction of physical space

Bounias¹,

Krasnoholovets

2003

Kybernetes

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An abstract lattice of empty set cells is shown to be able to account for a primary substrate in a physical space. Space-time is represented by ordered sequences of topologically closed Poincaré sections of this primary space. These mappings are constrained to provide homeomorphic structures serving as frames of reference in order to account for the successive positions of any objects present in the system. Mappings from one section to the next involve morphisms of the general structures, representing a continuous reference frame, and morphisms of objects present in the various parts of this structure. The combination of these morphisms provides space-time with the features of a non-linear generalized convolution. Discrete properties of the lattice allow the prediction of scales at which microscopic to cosmic structures should occur. Deformations of primary cells by exchange of empty set cells allow a cell to be mapped into an image cell in the next section as far as the mapped cells remain homeomorphic. However, if a deformation involves a fractal transformation to objects, there occurs a change in the dimension of the cell and the homeomorphism is not conserved. Then, the fractal kernel stands for a "particle" and the reduction of its volume (together with an increase in its area up to infinity) is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. The interactions of a moving particle-like deformation with the surrounding lattice involves a fractal decomposition process, which supports the existence and properties of previously postulated inerton clouds as associated to particles. Experimental evidence of the existence of inertons is reviewed and further possibilities of experimental proofs proposed.

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Section: Predictions Of Fundamental Physical Parametersmentioning

confidence: 99%

Scanning the structure of ill‐known spaces: Part 2. Principles of construction of physical space

Bounias¹,

Krasnoholovets

2003

Kybernetes

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“…This is enough to support lower levels of life organization. However, such fixed points can stand for mental images in a space organized as a brain‐type system (Bounias and Bonaly, 1997b; Bounias, 2000, Sharma et al , 2001). This denotes a higher level of organization in which greater levels are required:…”

Section: Remarks 31mentioning

confidence: 99%

Universe as a self‐observable, self‐ethical, life‐embedding mathematical system

Bounias¹

2002

Kybernetes

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The non‐well‐founded properties of the empty set provide existence to abstract topological spaces, in which intersections of subspaces with non‐equal dimensions give topologically closed structures. This let space‐time emerge as an ordered sequence of sections upon a defined combination rule, in which interactivity between observable structures is allowed and conditions for conscious perception phenomena are fulfilled. Conditions for evolution and rules for optimal evolution of ecosystems also infer as corollaries. A physical universe and life constitute one single self‐organized and self managed system where life appears as the physical‐like realization of conditions of functionality of the embedding mathematical spaces. The system includes self‐ethical and moral guidelines which should inspire human behavior on Planet Earth.

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“…Lastly, we are currently working on purely mathematical aspects of biology [22,23] in which semi-compatibility condition [11] could provide previously missing basis for the justification of some brain functions.…”

Section: -2mentioning

confidence: 99%

Fixed points for non‐surjective expansion mappings

Sharma

Sahu

Bounias

et al. 1997

International Journal of Mathematics and Mathematical Sciences

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The contractive conditions of Popa (Demonstr. Math. 1990, 23, 213-218) were further improved for four non-surjective expansion mappings, and some common fixed point theorems under semi-compatible pairs of mappings are proved. Our main findings bring improvements to a number of results in the non-metric setting. Some implications for mathematical physics are raised with respect to physical invariants.

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The topology of perceptive functions as a corollary of the theorem of existence in closed spaces

Cited by 8 publications

References 27 publications

Scanning the structure of ill‐known spaces: Part 2. Principles of construction of physical space

Scanning the structure of ill‐known spaces: Part 2. Principles of construction of physical space

Universe as a self‐observable, self‐ethical, life‐embedding mathematical system

Fixed points for non‐surjective expansion mappings

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