Axiomatic basis for spaces with noninteger dimension

@article{Stillinger1977AxiomaticBF,
  title={Axiomatic basis for spaces with noninteger dimension},
  author={Frank H. Stillinger},
  journal={Journal of Mathematical Physics},
  year={1977},
  volume={18},
  pages={1224-1234}
}
  • F. Stillinger
  • Published 1 June 1977
  • Mathematics
  • Journal of Mathematical Physics
Five structural axioms are proposed which generate a space SD with ’’dimension’’ D that is not restricted to the positive integers. Four of the axioms are topological; the fifth specifies an integration measure. When D is a positive integer, SD behaves like a conventional Euclidean vector space, but nonvector character otherwise occurs. These SD conform to informal usage of continuously variable D in several recent physical contexts, but surprisingly the number of mutually perpendicular lines… 

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