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I've heard $E$ is for entire space, $B$ is for base space, so what is $M$ for?

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No clue, manifold? –  Fernando Muro Apr 6 '12 at 10:04
    
I reckon E is not for "entire space", but for "étalé space" (étalé means "spread out"). –  Malte Apr 6 '12 at 11:44
    
Thom uses notation such as $M(SO(n))$ for the Thom space in his original papers, e.g., Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 28, (1954). 17–86. So presumably he is responsible for that notation. –  Charles Rezk Apr 6 '12 at 12:36
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$T$ was already taken for tangent bundle, so $M$ is a pretty good 2nd fiddle. –  Ryan Budney Apr 6 '12 at 19:38
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It seems that the earliest use is in Thom's paper: archive.numdam.org/article/SB_1951-1954__2__271_0.pdf –  John Klein Apr 6 '12 at 21:48
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