A new look at infinite matroids
نویسندگان
چکیده
It has recently been shown that, contrary to common belief, infinite matroids can be axiomatized in a way very similar to finite matroids. This should make it possible now to extend much of the theory of finite matroids to infinite ones: an aim that had previously been thought to be unattainable, because the popular additional ‘finitary’ axiom believed to be necessary clearly spoils duality. We present the five new axiom sets for infinite matroids found in [3]. They come in terms of independent sets, bases, circuits, closure and rank. We then illustrate them by showing what becomes of the usual cycle and bond matroids of a graph when this graph is infinite.
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