PTITeX 3.4, (c) Personal TeX, Inc. 1985-1998 This is TeX 3.14159 (preloaded format=LATEX 0.11.30) 10 JAN 2001 12:16 **&LATEX C:/FPhandbook/hyperconvex-revised.tex (C:\FPhandbook\hyperconvex-revised.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, loaded. (C:\PCTeXv4\AMSLTX12\amsart.cls Document Class: amsart 1995/02/23 v1.2b \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (C:\PCTeXv4\AMSLTX12\amsgen.sty File: amsgen.sty 1995/02/01 v1.2a \@emptytoks=\toks14 \ex@=\dimen104 ) (C:\PCTeXv4\AMSLTX12\amsmath.sty Package: amsmath 1995/02/23 v1.2b AMS math features \@mathmargin=\skip42 (C:\PCTeXv4\AMSLTX12\amstext.sty Package: amstext 1995/01/25 v1.2 ) (C:\PCTeXv4\AMSLTX12\amsbsy.sty Package: amsbsy 1995/01/20 v1.2 \pmbraise@=\dimen105 ) (C:\PCTeXv4\AMSLTX12\amsopn.sty Package: amsopn 1995/02/20 v1.2a operator names ) LaTeX Info: Redefining \frac on input line 180. \uproot@=\count79 \leftroot@=\count80 \classnum@=\count81 \DOTSCASE@=\count82 LaTeX Info: Redefining \dots on input line 327. LaTeX Info: Redefining \ldots on input line 410. LaTeX Info: Redefining \cdots on input line 414. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen106 LaTeX Font Info: Redeclaring font encoding OML on input line 492. LaTeX Font Info: Redeclaring font encoding OMS on input line 493. \skewcharcount@=\count83 \familycount@=\count84 \pointcount@=\count85 \accentdimen@=\dimen107 \accentmu@=\count86 \minaw@=\dimen108 \c@MaxMatrixCols=\count87 \dotsspace@=\muskip10 \c@parentequation=\count88 \dspbrk@lvl=\count89 \tag@help=\toks15 \row@=\count90 \column@=\count91 \maxfields@=\count92 \andhelp@=\toks16 \eqnshift@=\dimen109 \alignsep@=\dimen110 \tagshift@=\dimen111 \tagwidth@=\dimen112 \totwidth@=\dimen113 \lineht@=\dimen114 \@envbody=\toks17 \multlinegap=\skip43 \multlinetaggap=\skip44 ) (C:\PCTeXv4\AMSLTX12\amsfonts.sty Package: amsfonts 1995/02/01 v2.2b \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 128. ) \copyins=\insert233 \abstractbox=\box28 \listisep=\skip45 \c@part=\count93 \c@section=\count94 \c@subsection=\count95 \c@subsubsection=\count96 \c@paragraph=\count97 \c@figure=\count98 \c@table=\count99 \abovecaptionskip=\skip46 \belowcaptionskip=\skip47 (C:\PCTeXv4\AMSLTX12\amsthm.sty Package: amsthm 1995/02/01 v1.2a \theorem@style=\toks18 \theorembodyfont=\toks19 \theoremheadfont=\toks20 \theoremnotefont=\toks21 \theoremheadpunct=\toks22 \theorempreskipamount=\skip48 \theorempostskipamount=\skip49 )) (C:\PCTeXv4\AMSLTX12\amssymb.sty Package: amssymb 1995/02/01 v2.2a ) (C:\PCTeXv4\LATEX2E\newlfont.sty Package: newlfont 1998/08/17 v2.2m Standard LaTeX package LaTeX Info: Redefining \em on input line 49. (C:\PCTeXv4\LATEX2E\latexsym.sty Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols) \symlasy=\mathgroup6 LaTeX Font Info: Overwriting symbol font `lasy' in version `bold' (Font) U/lasy/m/n --> U/lasy/b/n on input line 29. )) (C:\PCTeXv4\LATEX2E\inputenc.sty beta test version Package: inputenc 1998/03/05 v0.97 Input encoding file (test version: still lia ble to change) (C:\PCTeXv4\LATEX2E\ansinew.def File: ansinew.def 1998/03/05 v0.97 Input encoding file (test version: still lia ble to change) )) (C:\PCTeXv4\LATEX2E\graphicx.sty Package: graphicx 1997/06/09 v1.0d Enhanced LaTeX Graphics (DPC,SPQR) (C:\PCTeXv4\LATEX2E\keyval.sty Package: keyval 1998/06/05 v1.11 key=value parser (DPC) \KV@toks@=\toks23 ) (C:\PCTeXv4\LATEX2E\graphics.sty Package: graphics 1998/05/27 v1.0h Standard LaTeX Graphics (DPC,SPQR) (C:\PCTeXv4\LATEX2E\trig.sty Package: trig 1994/10/16 v1.08 sin cos tan (DPC) ) (C:\PCTeXv4\LATEX2E\graphics.cfg) Package graphics Info: Driver file: dvips.def on input line 85. (C:\PCTeXv4\LATEX2E\dvips.def File: dvips.def 1998/05/03 v3.0f Driver-dependant file (DPC,SPQR) )) \Gin@req@height=\dimen115 \Gin@req@width=\dimen116 ) \c@theorem=\count100 ! LaTeX Error: Command \proof already defined. Or name \end... illegal, see p.192 of the manual. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.38 ...xtbf{#1.} }{\ \rule{0.5em}{0.5em}} ? \@indexfile=\write3 Writing index file hyperconvex-revised.idx LaTeX Warning: Unused global option(s): [showkey]. (C:/FPhandbook/hyperconvex-revised.aux) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 45. LaTeX Font Info: ... okay on input line 45. LaTeX Font Info: Try loading font information for U+msa on input line 45. (C:\PCTeXv4\AMSLTX12\umsa.fd File: Umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 45. (C:\PCTeXv4\AMSLTX12\umsb.fd File: Umsb.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+lasy on input line 45. (C:\PCTeXv4\LATEX2E\ulasy.fd File: ulasy.fd 1998/08/17 v2.2eLaTeX symbol font definitions ) (C:/FPhandbook/hyperconvex-revised.toc) \tf@toc=\write4 Underfull \hbox (badness 10000) in paragraph at lines 77--90 [] Underfull \hbox (badness 10000) in paragraph at lines 91--101 [] Underfull \hbox (badness 10000) in paragraph at lines 102--112 [] [1] Underfull \hbox (badness 10000) in paragraph at lines 113--143 [] Underfull \hbox (badness 10000) in paragraph at lines 144--170 [] Underfull \hbox (badness 10000) in paragraph at lines 185--194 [] Underfull \vbox (badness 10000) has occurred while \output is active [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [2] Underfull \hbox (badness 10000) in paragraph at lines 253--257 [] Underfull \hbox (badness 10000) in paragraph at lines 260--262 [] Underfull \hbox (badness 10000) in paragraph at lines 265--270 [] [3] Underfull \hbox (badness 10000) in paragraph at lines 274--280 [] Underfull \hbox (badness 10000) in 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[] Underfull \hbox (badness 10000) in paragraph at lines 897--906 [] Underfull \hbox (badness 10000) in paragraph at lines 909--915 [] Underfull \hbox (badness 10000) in paragraph at lines 924--928 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [10] Underfull \hbox (badness 10000) in paragraph at lines 932--937 [] Underfull \hbox (badness 10000) in paragraph at lines 940--945 [] Underfull \hbox (badness 10000) in paragraph at lines 956--959 [] Underfull \hbox (badness 10000) in paragraph at lines 964--966 [] Underfull \hbox (badness 10000) in paragraph at lines 1007--1012 [] [11] Underfull \hbox (badness 10000) in paragraph at lines 1037--1042 [] Underfull \hbox (badness 10000) in paragraph at lines 1051--1058 [] Underfull \hbox (badness 10000) in paragraph at lines 1066--1071 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [12] Underfull \hbox (badness 10000) in paragraph at lines 1115--1123 [] Underfull \hbox (badness 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(badness 10000) in paragraph at lines 2319--2323 [] Underfull \hbox (badness 10000) in paragraph at lines 2334--2338 [] Underfull \hbox (badness 10000) in paragraph at lines 2355--2360 [] [27] Underfull \hbox (badness 10000) in paragraph at lines 2368--2371 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [28] [29] Underfull \hbox (badness 10000) in paragraph at lines 2512--2516 [] Underfull \hbox (badness 10000) in paragraph at lines 2518--2528 [] Underfull \hbox (badness 10000) in paragraph at lines 2543--2546 [] Package amsfonts Warning: Obsolete command \frak; \mathfrak should be used inst ead on input line 2565. LaTeX Font Info: Try loading font information for U+euf on input line 2565. (C:\PCTeXv4\AMSLTX12\ueuf.fd File: Ueuf.fd 1995/01/05 v2.2e AMS font definitions ) Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [30] Underfull \hbox (badness 10000) in paragraph at lines 2629--2638 [] Underfull \hbox (badness 10000) in paragraph at lines 2643--2647 [] Overfull \hbox (1.1535pt too wide) in paragraph at lines 2672--2678 []\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 H$ \OT1/cmr/m/it/10 be hy-per-con-vex, let $\OML/cmm/m/it/10 T[] \OT1/cmr/m/n/10 : \OML/cmm/m/it/10 H \OMS/cmsy/m/n/1 0 ! E\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 H\OT1/cmr/m/n/10 )$ \OT1/cmr/m/it/10 be non-ex-pan-sive and sup-pose $[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 T[]\OT1/cmr/m /n/10 ) \OMS/cmsy/m/n/10 6\OT1/cmr/m/n/10 = [] [31] Underfull \hbox (badness 10000) in paragraph at lines 2744--2752 [] Underfull \hbox (badness 10000) in paragraph at lines 2753--2773 [] Underfull \hbox (badness 10000) in paragraph at lines 2780--2785 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [32] Underfull \hbox (badness 10000) in paragraph at lines 2831--2837 [] Underfull \hbox (badness 10000) in paragraph at lines 2854--2862 [] Underfull \hbox (badness 10000) in paragraph at lines 2874--2877 [] Underfull \hbox (badness 10000) in paragraph at lines 2884--2889 [] [33] Underfull \hbox (badness 10000) in paragraph at lines 2926--2930 [] Underfull \hbox (badness 10000) in paragraph at lines 2936--2939 [] Underfull \hbox (badness 10000) in paragraph at lines 2947--2956 [] Underfull \hbox (badness 10000) in paragraph at lines 2959--2966 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [34] Underfull \hbox (badness 10000) in paragraph at lines 3003--3008 [] Underfull \hbox (badness 10000) in paragraph at lines 3018--3022 [] Underfull \hbox (badness 10000) in paragraph at lines 3027--3031 [] Underfull \hbox (badness 10000) in paragraph at lines 3048--3052 [] Underfull \hbox (badness 10000) in paragraph at lines 3064--3068 [] [35] Underfull \hbox (badness 10000) in paragraph at lines 3099--3106 [] Underfull \hbox (badness 10000) in paragraph at lines 3113--3114 [] Overfull \hbox (2.77399pt too wide) in paragraph at lines 3151--3157 \OT1/cmr/m/n/10 Therefore, $\OML/cmm/m/it/10 r\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 c[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 62 [] \OML/cmm/m/it/10 G\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 )$ and $\OML/cmm/m/it/10 r\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 c[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2 []\OT1/cmr/m/n/10 (\O MS/cmsy/m/n/10 f\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ; \OML/cmm/m/it/10 i \OMS/c msy/m/n/10 2 \OML/cmm/m/it/10 I\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 )$, con-tra-di ct-ing the as-sump-tion $[](\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/ 10 ; \OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 2 [] Underfull \hbox (badness 10000) in paragraph at lines 3151--3157 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [36] Underfull \hbox (badness 10000) in paragraph at lines 3171--3172 [] Underfull \hbox (badness 10000) in paragraph at lines 3176--3180 [] Underfull \hbox (badness 10000) in paragraph at lines 3195--3196 [] Underfull \hbox (badness 10000) in paragraph at lines 3202--3210 [] Underfull \hbox (badness 10000) in paragraph at lines 3221--3228 [] Underfull \hbox (badness 10000) in paragraph at lines 3230--3237 [] [37] Underfull \hbox (badness 10000) in paragraph at lines 3265--3269 [] Underfull \hbox (badness 10000) in paragraph at lines 3278--3288 [] Underfull \hbox (badness 10000) in paragraph at lines 3299--3303 [] Underfull \hbox (badness 10000) in paragraph at lines 3307--3311 [] Underfull \hbox (badness 10000) in paragraph at lines 3325--3329 [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [38] Underfull \hbox (badness 10000) in paragraph at lines 3345--3346 [] Underfull \hbox (badness 10000) in paragraph at lines 3351--3358 [] Underfull \hbox (badness 10000) in paragraph at lines 3359--3370 [] Underfull \hbox (badness 10000) in paragraph at lines 3372--3375 [] Underfull \hbox (badness 10000) in paragraph at lines 3400--3407 [] [39] Underfull \vbox (badness 10000) has occurred while \output is active [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [40] Package amsfonts Warning: Obsolete command \bold; \mathbf should be used instea d on input line 3619. [41] (C:/FPhandbook/hyperconvex-revised.aux) ) Here is how much of TeX's memory you used: 1958 strings out of 2873 20272 string characters out of 28518 13959 words of memory out of 73728 4619 multiletter control sequences out of 10000 13442 words of font info for 54 fonts, out of 20000 for 255 176 hyphenation exceptions out of 607 34i,15n,32p,294b,414s stack positions out of 200i,40n,60p,5000b,600s Output written on C:\FPhandbook\hyperconvex-revised.dvi (41 pages, 216240 bytes ).