IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i1p530-531.html
   My bibliography  Save this article

On the mathematical theory of transfinite dimensions and its application in physics

Author

Listed:
  • Nada, S.I.

Abstract

Following the mathematical theory of infinite dimensional spaces, we introduce basic definitions and theorems. We show that the three different fundamental notions of dimension coincide only for separable metric spaces. Subsequently, the degree of infinite dimensionality is considered, which leads us to the notion of transfinite dimensions and the introduction of stratification to a wide class of spaces. These particular spaces are the main subject of E-infinity theory of high energy physics.

Suggested Citation

  • Nada, S.I., 2009. "On the mathematical theory of transfinite dimensions and its application in physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 530-531.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:530-531
    DOI: 10.1016/j.chaos.2009.01.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909000241
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.01.029?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    2. El Naschie, M.S., 2009. "The theory of Cantorian spacetime and high energy particle physics (an informal review)," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2635-2646.
    3. Elokaby, A., 2009. "On the deep connection between instantons and string states encoder in Klein’s modular space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 303-305.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marek-Crnjac, L. & Iovane, G. & Nada, S.I. & Zhong, Ting, 2009. "The mathematical theory of finite and infinite dimensional topological spaces and its relevance to quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1974-1979.
    2. Nada, S.I., 2009. "Density manifolds, geometric measures and high-energy physics in transfinite dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1539-1541.
    3. Marek-Crnjac, L., 2009. "Partially ordered sets, transfinite topology and the dimension of Cantorian-fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1796-1799.
    4. Iovane, G., 2009. "From Menger–Urysohn to Hausdorff dimensions in high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2338-2341.
    5. El-Nabulsi, Ahmad Rami, 2009. "Complexified quantum field theory and “mass without mass” from multidimensional fractional actionlike variational approach with dynamical fractional exponents," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2384-2398.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wu, Guo-Cheng & He, Ji-Huan, 2009. "On the Menger–Urysohn theory of Cantorian manifolds and transfinite dimensions in physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 781-783.
    2. Zhong, Ting, 2009. "From the numerics of dynamics to the dynamics of numerics and visa versa in high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1780-1783.
    3. Marek-Crnjac, L., 2009. "Partially ordered sets, transfinite topology and the dimension of Cantorian-fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1796-1799.
    4. Iovane, G., 2009. "From Menger–Urysohn to Hausdorff dimensions in high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2338-2341.
    5. Nada, S.I., 2009. "Density manifolds, geometric measures and high-energy physics in transfinite dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1539-1541.
    6. Marek-Crnjac, L. & Iovane, G. & Nada, S.I. & Zhong, Ting, 2009. "The mathematical theory of finite and infinite dimensional topological spaces and its relevance to quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1974-1979.
    7. Elokaby, A., 2009. "On the deep connection between instantons and string states encoder in Klein’s modular space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 303-305.
    8. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    9. El Naschie, M.S., 2009. "The theory of Cantorian spacetime and high energy particle physics (an informal review)," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2635-2646.
    10. He, Ji-Huan, 2009. "Hilbert cube model for fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2754-2759.
    11. Halayka, S., 2009. "Associating disconnectedness with electromagnetic phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 469-471.
    12. El Naschie, M.S., 2009. "On zero-dimensional points curvature in the dynamics of Cantorian-fractal spacetime setting and high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2725-2732.
    13. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    14. Nada, S.I. & Hamouda, E.H., 2009. "Fundamental group of dual graphs and applications to quantum space time," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 500-503.
    15. Esmaeili, M. & Gulliver, T.A. & Kakhbod, A., 2009. "The Golden mean, Fibonacci matrices and partial weakly super-increasing sources," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 435-440.
    16. Marek-Crnjac, L., 2009. "A Feynman path integral-like method for deriving the four dimensionality of spacetime from first principles," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2471-2473.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:530-531. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.