An article in the current issue of American Mathematical MONTHLY (G. Folland, "A tale of topology," Am. Math. Monthly 117 (8) pp.663-672, Oct. 2010) quotes Walter Rudin as follows:
Thus it appears that Čech proved the Tychonoff theorem, whereas Tychonoff found the Čech compactification -- a good illustration of the historical reliability of mathematical nomenclature.
Folland's article suggests the truth is more complicated, as it usually is.