Abstract
Four exchange properties, including the usual one, are discussed. Assuming the finiteness condition or a weaker condition (called minimal condition), all four are equivalent. But examples show that in general no two of the four properties are equivalent. Furthermore it is shown that all four properties and the minimal condition follow from the Existence Theorem for a basis.
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Kreuzer, A., Sörensen, K. Exchange properties in closure spaces. J. Geom. 98, 127–138 (2010). https://doi.org/10.1007/s00022-010-0049-8
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DOI: https://doi.org/10.1007/s00022-010-0049-8