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On linear spaces and matroids of arbitrary cardinality

✍ Scribed by Dieter Betten; Walter Wenzel

Publisher
Springer
Year
2003
Tongue
English
Weight
383 KB
Volume
49
Category
Article
ISSN
0002-5240

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πŸ“œ SIMILAR VOLUMES

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It was proved by Dow and Simon that there are 2"' (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height WI and width w. In this paper, we prove that if cy is an ordinal with WI < 01 < w2 and 19 = (KC: [ < cx) is a sequence of cardinals such that either KC = w or KC =

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Let V be a linear space of even dimension n over a field F of characteristic 0. A subspace W βŠ‚ ∧ 2 V is maximal singular if rank(w) ≀ n -1 for all w ∈ W and any W W βŠ‚ ∧ 2 V contains a nonsingular matrix. It is shown that if W βŠ‚ ∧ 2 V is a maximal singular subspace which is generated by decomposable