# 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} }

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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