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) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
