Errata and addenda to July 2007 and March 2008 preprints of "Mapping radii of metric spaces" by George M. Bergman

Pacific Journal of Mathematics, 236 (2008) 223-261.

Corrections to July 2007 print, fixed in March 2008 print

P.10, display (30) and preceding sentence:  Symmetry in the subscripts does not, as I claimed, show that  d( p, f(yi)) = d( p, f(y0)),  etc..  Rather, it shows that in bounding  d( p, f(yi)),  etc., we can without loss of generality assume  i = 0. 

P.17: In the statement of Corollary 26, we must assume not only that  D(\nu) = \mu,  but that  \nu  has the same positive and negative supports as  \mu,  and that  \Gamma(\nu)  is cycle-free.  (The words "By Proposition 24" can then be dropped from the proof.) 

Further note:

One new result was added in the March 2008 print, Lemma 33, p.22, which says that if  X  is a bounded subset of a normed vector space  V,  then the infimum, over all normed vector spaces  W  containing  V,  of  rad W (X),  is given by   rad V { (x-y) / 2 | x, y \in X }.  As indicated below, in the published version it is noted that this also equals  diam(X) / 2. 

Corrections that apply to both the above preprints

Important corrections

P.8 or 9, last sentence of proof of Corollary 14:  1 - max(d(x0,x), 1)  should be  1 - min(d(x0,x), 1). 

P.10:  In the lines following display (25), "maximize" should in both places be "minimize", and "infimum" should be "supremum".  The line after display (26) should be expanded to:  "Writing  ex , ey , ez  respectively for the functions on  X  given by the integral in (16) for these three measures  \mu,  we find that".  Then, in display (27), change all 9 instances of  \mu  to  e;  and likewise, in the paragraph between (28) and (29), change all 5 instances of  \mu  to  e.  (But no change needed in the paragraph between (27) and (28).) 

Minor clarifications

Statement of Lemma 5:  change "preserve  A" to "carry  A  into itself ".  (To avoid the possible misinterpretation "fix  A  pointwise.") 

Statement of Lemma 7:  The reference to  V  and  V'  in the first sentence can be dropped:  They never appear after that! 

In the 5th line before Question 23,  Sn  should be  Sn. 

In the 3rd line after the proof of Propositon 24,  after "is achieved" add "and that the other parameters mentioned above can then be minimized;". 

Addendum to March 2008 preprint

P.22, statement of Lemma 33:  Add to display (47) the additional equality:  = diam(X) / 2. 
This extended statement actually has a slightly simpler proof than the earlier version.  (Details in final preprint and published article.) 

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