Expanding topological space,study and applications |
| |
Authors: | Hélène Porchon |
| |
Institution: | UFR 929 Mathématiques, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France |
| |
Abstract: | In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to any fractal family of topological spaces is expanding. In particular, we prove that the more a topological space expands, the finer the topology of its indexed states is. Using multi-homeomorphisms over associated coproduct topological spaces, we define a locally expandable topological space and we prove that a locally expandable topological space has a topological expansion. Specifically, we prove that the fractal manifold is locally expandable and has a topological expansion. |
| |
Keywords: | 54A05 54A10 54D80 54F65 54H20 |
本文献已被 ScienceDirect 等数据库收录! |
|