# Corrections to “Winding Around”

• Page 24, Figure 2.1; the coordinate $$\phi(P)$$ should be $$x/(1-y)$$, not $$y/(1-x)$$.
• Page 123, Displayed equation in the proof of Proposition 7.1.3, $$\sum \lambda_i v_i$$ should be $$\sum \lambda_i w_i$$.
• Page 137, Exercise 7.5.5 the display $$\int k(x,y) f(x)$$ should read $$\int k(x,y) f(y) dy$$.  The rest of the question is unchanged (this integral appears only in an explanatory historical aside)
• Page 217, last line.  Insert the word “distinct” after “all”

Regarding footnote 1 (page 54), Robert Burckel drew my attention to the note On sandwich slicing by R. Arens (Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), pp. 57–60,
Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam-New York, 1980.  This shows that this continuity may fail if we give the phrase “solid body” too generous an interpretation (specifically, if it is unbounded but of finite measure).  This improves the statement of the footnote: it is better to say “this can fail under certain circumstances” (with an explicit counterexample) than “we ought to sweat about this”.  The argument in the exercise referenced by this footnote is for bounded regions and is not affected by this example.