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MR1189542 (94d:15022) 15A54 (54D05)
Evard, J.-Cl.; Jafari, F. The set of all $m\times n$ rectangular real matrices of rank $r$ is connected by analytic regular arcs. Proc. Amer. Math. Soc. 120 (1994), no. 2, 413–419.
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