Abstract
It is shown that the homology and cohomology groups of a regular nearness space can be defined by means of a variation on the Čech method, which uses nerves of uniform covers: the variation involves associating with each uniform cover, not the nerve, but a complex, called the vein, defined by means of nearness.
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Bibliography
H. L. Bentley, Homology and cohomology for merotopic and nearness spaces, preprint.
D. Czarcinski, The Čech Homology Theory for Nearness Spaces, Dissertation, University of Toledo (1975).
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H. Herrlich, A concept of nearness, General Topology and Appl. 4 (1974) 191–212.
H. Herrlich, Topological structures, In: Topological Structures, Math. Centre Tracts 52, Amsterdam (1974) 59–122.
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© 1982 Springer-Verlag
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Bentley, H.L. (1982). A note on the homology of regular nearness spaces. In: Kamps, K.H., Pumplün, D., Tholen, W. (eds) Category Theory. Lecture Notes in Mathematics, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066879
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DOI: https://doi.org/10.1007/BFb0066879
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