Fractal topology foundations. (English) Zbl 1306.54004
In this paper, the author introduces the concept of fractal topology in such a way that a fractal manifold (as defined in [F. Ben Adda, Int. J. Pure Appl. Math. 38, No. 2, 155–186 (2007; Zbl 1151.58001)]) has locally a fractal topology.
Reviewer: Miguel Angel Sanchez Granero (Almería)
MSC:
54A05 | Topological spaces and generalizations (closure spaces, etc.) |
54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
54D80 | Special constructions of topological spaces (spaces of ultrafilters, etc.) |
54F65 | Topological characterizations of particular spaces |
Citations:
Zbl 1151.58001References:
[1] | Ben Adda, F., Mathematical model for fractal manifold, Int. J. Pure Appl. Math., 38, 2, 159-190 (2007) |
[2] | Ben Adda, F., New understanding of the dark energy in the light of new space-time, (Invisible Universe: Proceeding of the Conference. Invisible Universe: Proceeding of the Conference, AIP Conf. Proc., vol. 1241 (2010)), 487-496 |
[3] | Edgar, G. A., Measure, Topology and Fractal Geometry, Undergrad. Texts Math. (2008), Springer · Zbl 1152.28008 |
[4] | Montiel, M. E.; Aguado, A. S.; Zaluska, E., Topology in fractals, Chaos Solitons Fractals, 7, 8, 1187-1201 (1996), 1203-1207 · Zbl 1080.28503 |
[5] | Song, C.; Havlin, S.; Makse, H. A., Origins of fractality in the growth of complex networks, Nature Phys., 2, 275-281 (2006) |
[6] | Wheeler, J. A., Geometrodynamics (1962), Academic Press: Academic Press New York · Zbl 0124.22207 |
[7] | Zelenyi, M.; Milovanov, A. V., Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics, Phys. Usp., 47, 749 (2004) |
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