Abstract
The definitions of fuzzy and hazy spaces are reviewed and consideration is given to using these spaces for representing physical phenomena. Two primitive situations are studied: the description of interactions among particles and the description of directions. It is shown that when a representation of discrete interactions is reduced to essentials a distributive lattice with a fuzzy space structure emerges quite naturally. To represent directions in a space with fairly arbitrary underlying structure, the hazy analogue of a differentiable manifold is required. Every point in a hazy space has associated with it a collection of subsets. The free group on these immediately gives a module over the integers as a tangent space at the point. Moreover the neighbourhood of each point has a chart map taking values in the module. By this means points are coordinatized and directions in the space can be described.
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Dodson, C.T.J. Fuzzy interactions and hazy directions. Lett Math Phys 1, 75–82 (1975). https://doi.org/10.1007/BF00405590
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DOI: https://doi.org/10.1007/BF00405590