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LaTeX Warning: Label `' multiply defined. LaTeX Warning: Label `' multiply defined. LaTeX Warning: Label `' multiply defined. LaTeX Warning: Label `' multiply defined. LaTeX Warning: Label `' multiply defined. ) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for IL2/cmr/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 43. LaTeX Font Info: ... okay on input line 43. LaTeX Font Info: Try loading font information for U+msa on input line 48. (c:/emtex/texinput/amsfonts/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 48. (c:/emtex/texinput/amsfonts/umsb.fd File: Umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] [2 ] (ect.toc [3] Underfull \hbox (badness 10000) in paragraph at lines 37--37 [][] [] \OT1/cmr/m/n/10 Var-i-ous kind-s of con-nect-ed-ness ($\OML/cmm/m/it/1 0 ^^U$\OT1/cmr/m/n/10 -connectedness, [] [4] [5]) \tf@toc=\write5 [6] Chapter 0. [7 ] [8 ] Chapter 1. Package amsfonts Warning: Obsolete command \Bbb; \mathbb should be used instead on input line 388. LaTeX Font Info: Try loading font information for OMS+cmr on input line 409. (c:/emtex/texinput/latex2e/omscmr.fd File: omscmr.fd 1997/01/14 v2.5a Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 409. [9] Underfull \hbox (badness 2707) in paragraph at lines 458--460 []\OT1/cmr/m/n/10 If $\OML/cmm/m/it/10 m$ \OT1/cmr/m/n/10 is the or-der of a ra m-i-fi-ca-tion point in a den-drite, then [] LaTeX Font Info: Try loading font information for U+euf on input line 460. (c:/emtex/texinput/amsfonts/ueuf.fd File: Ueuf.fd 1995/01/05 v2.2e AMS font definitions ) [10] File: ../s/c0001/s0020/e0030/A.eps Graphic file (type eps) <../s/c0001/s0020/e0030/A.eps> File: ../s/c0001/s0020/e0040/A.eps Graphic file (type eps) <../s/c0001/s0020/e0040/A.eps> File: ../s/c0001/s0020/e0040/B.eps Graphic file (type eps) <../s/c0001/s0020/e0040/B.eps> [11] [12] File: ../s/c0001/s0020/e0060/A.eps Graphic file (type eps) <../s/c0001/s0020/e0060/A.eps> Underfull \hbox (badness 10000) in paragraph at lines 685--688 []$\OML/cmm/m/it/10 D[]$ \OT1/cmr/m/n/10 is ho-mo-ge-neous with re-spec-t to mo no-tone map-pings, [] [13] File: ../s/c0001/s0020/e0070/A.eps Graphic file (type eps) <../s/c0001/s0020/e0070/A.eps> File: ../s/c0001/s0020/e0070/B.eps Graphic file (type eps) <../s/c0001/s0020/e0070/B.eps> File: ../s/c0001/s0020/e0070/C.eps Graphic file (type eps) <../s/c0001/s0020/e0070/C.eps> [14] [15] [16] Underfull \hbox (badness 10000) in paragraph at lines 833--835 []\OT1/cmr/m/n/10 The fol-low-ing prop-er-ties of den-drites $\OML/cmm/m/it/10 D[]$ \OT1/cmr/m/n/10 are known (see [] Underfull \hbox (badness 1043) in paragraph at lines 852--855 []\OT1/cmr/m/n/10 For any nonemp-ty sub-set $\OML/cmm/m/it/10 S \OMS/cmsy/m/n/1 0 ^^Z f\OT1/cmr/m/n/10 3\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 4\OML/cmm/m/it/10 ; [] ; !\OMS/cmsy/m/n/10 g$ \OT1/cmr/m/n/10 and for an ar-bi-trary [] Underfull \hbox (badness 2103) in paragraph at lines 852--855 \OT1/cmr/m/n/10 den-drite $\OML/cmm/m/it/10 Y$ \OT1/cmr/m/n/10 there ex-ist-s a mono-tone map-ping from $\OML/cmm/m/it/10 D[]$ \OT1/cmr/m/n/10 on-to $\OML/cmm /m/it/10 Y$\OT1/cmr/m/n/10 , [] [17] Underfull \hbox (badness 10000) in paragraph at lines 908--912 []\OT1/cmr/m/n/10 The fol-low-ing prop-er-ties of the [][]\OT1/cmr/m/it/10 den- drite $\OML/cmm/m/it/10 P$ \OT1/cmr/m/n/10 are proved in [] File: ../s/c0001/s0020/e0090/A.eps Graphic file (type eps) <../s/c0001/s0020/e0090/A.eps> Underfull \hbox (badness 10000) in paragraph at lines 952--964 []\OT1/cmr/m/n/10 There is a strong-ly point-wise self-homeomorphic den-drite [] Underfull \hbox (badness 1983) in paragraph at lines 952--964 \OT1/cmr/m/n/10 which is not of the for-m $\OML/cmm/m/it/10 D[]$ \OT1/cmr/m/n/1 0 for some $\OML/cmm/m/it/10 S \OMS/cmsy/m/n/10 ^^Z f\OT1/cmr/m/n/10 3\OML/cmm/ m/it/10 ; \OT1/cmr/m/n/10 4\OML/cmm/m/it/10 ; [] ; !\OMS/cmsy/m/n/10 g$\OT1/cmr /m/n/10 , see [] File: ../s/c0001/s0020/e0100/A.eps Graphic file (type eps) <../s/c0001/s0020/e0100/A.eps> Overfull \hbox (19.36125pt too wide) in paragraph at lines 965--965 [] [] [18] Underfull \hbox (badness 3826) in paragraph at lines 968--973 \OT1/cmr/m/n/10 den-drite which is not strong-ly point-wise self-homeomorphic, see [] File: ../s/c0001/s0020/e0100/B.eps Graphic file (type eps) <../s/c0001/s0020/e0100/B.eps> Overfull \hbox (20.36499pt too wide) in paragraph at lines 981--981 [] [] [19] [20] [21] File: ../s/c0001/s0020/e0120/A.eps Graphic file (type eps) <../s/c0001/s0020/e0120/A.eps> Underfull \hbox (badness 10000) in paragraph at lines 1058--1060 []\OT1/cmr/m/n/10 The Omil-janows-ki den-drite $\OML/cmm/m/it/10 L[]$ \OT1/cmr/ m/n/10 has the fol-low-ing prop-er-ties, [] Underfull \hbox (badness 4391) in paragraph at lines 1069--1073 []\OT1/cmr/m/n/10 The fol-low-ing con-di-tion-s are e-quiv-a-len-t for a den-dr ite $\OML/cmm/m/it/10 X$ \OT1/cmr/m/n/10 (see [] [22] Underfull \hbox (badness 3168) in paragraph at lines 1078--1080 []$\OML/cmm/m/it/10 X$ \OT1/cmr/m/n/10 is mono-tone-ly e-quiv-a-len-t to $\OML/ cmm/m/it/10 D[]$ \OT1/cmr/m/n/10 for each nonemp-ty set [] [23] Underfull \hbox (badness 10000) in paragraph at lines 1220--1223 \OT1/cmr/m/n/10 An ex-am-ple of a rigid den-drite has been rough-ly de-scribed in [] Underfull \hbox (badness 2401) in paragraph at lines 1220--1223 \OT1/cmr/m/n/10 [[]]. It-s con-struc-tion is re-called be-low (see al-so [] [24] File: ../s/c0001/s0020/e0150/A.eps Graphic file (type eps) <../s/c0001/s0020/e0150/A.eps> [25] [26] File: ../s/c0001/s0020/e0180/A.eps Graphic file (type eps) <../s/c0001/s0020/e0180/A.eps> Underfull \hbox (badness 10000) in paragraph at lines 1451--1453 \OT1/cmr/m/n/10 The con-cep-t of the Gehman den-drite has been gen-er-al-ized i n [] [27] File: ../s/c0001/s0020/e0190/A.eps Graphic file (type eps) <../s/c0001/s0020/e0190/A.eps> [28] [29] Underfull \hbox (badness 2042) in paragraph at lines 1613--1621 \OT1/cmr/m/n/10 u-ni-ver-sal in the class of al-l $(\OML/cmm/m/it/10 m \OMS/cms y/m/n/10 ^^@ \OT1/cmr/m/n/10 1)$-dimensional sub-set-s of $\U/msb/m/n/10 R[]$ [] Underfull \hbox (badness 1158) in paragraph at lines 1630--1636 []\OT1/cmr/m/n/10 A con-tin-u-um $\OML/cmm/m/it/10 X$ \OT1/cmr/m/n/10 is home-o -mor-phic to $\OML/cmm/m/it/10 M[]$ \OT1/cmr/m/n/10 if and on-ly if $\OML/cmm/m /it/10 X$ \OT1/cmr/m/n/10 is [] Underfull \hbox (badness 1442) in paragraph at lines 1637--1644 []\OT1/cmr/m/n/10 Equivalently, $\OML/cmm/m/it/10 X$ \OT1/cmr/m/n/10 is home-o- mor-phic to $\OML/cmm/m/it/10 M[]$ \OT1/cmr/m/n/10 if and on-ly if $\OML/cmm/m/ it/10 X$ \OT1/cmr/m/n/10 is [] Underfull \hbox (badness 1389) in paragraph at lines 1679--1681 []$\OML/cmm/m/it/10 M[] \OMS/cmsy/m/n/10 ^^B \OML/cmm/m/it/10 X$ \OT1/cmr/m/n/1 0 is not 2-homogeneous for an ar-bi-trary con-tin-u-um $\OML/cmm/m/it/10 X$ [] [30] Underfull \hbox (badness 4859) in paragraph at lines 1694--1696 []\OT1/cmr/m/n/10 The Pol-ish group of au-to-home-o-mor-phism-s of $\OML/cmm/m/ it/10 M[]$ \OT1/cmr/m/n/10 is at most [] Underfull \hbox (badness 10000) in paragraph at lines 1698--1701 []\OT1/cmr/m/n/10 The group of au-to-home-o-mor-phism-s of $\OML/cmm/m/it/10 M[ ]$ \OT1/cmr/m/n/10 is sim-ple (see [] File: ../s/c0001/s0030/e0050/A.eps Graphic file (type eps) <../s/c0001/s0030/e0050/A.eps> [31] [32] Underfull \hbox (badness 5460) in paragraph at lines 1811--1818 \OT1/cmr/m/n/10 pla-nar lo-cal-ly con-nect-ed curve ad-mit-ting such a de-com-p o-si-tion [] Underfull \hbox (badness 1005) in paragraph at lines 1831--1834 []$\OML/cmm/m/it/10 M[]$ \OT1/cmr/m/n/10 is ho-mo-ge-neous with re-spec-t to th e class of sim-ple map-pings [] [33] Underfull \hbox (badness 2941) in paragraph at lines 1886--1890 \OT1/cmr/m/n/10 [[]]. Oth-er de-scrip-tion-s can be found in 1.4.1[] (see al-so [] File: ../s/c0001/s0030/e0060/A.eps Graphic file (type eps) <../s/c0001/s0030/e0060/A.eps> Overfull \hbox (13.33875pt too wide) in paragraph at lines 1891--1891 [] [] Underfull \hbox (badness 10000) in paragraph at lines 1914--1917 \OT1/cmr/m/n/10 non-locally-separating ar-c and has emp-ty in-te-ri-or in $\OML /cmm/m/it/10 X$ [] [34] [35] [36] Chapter 2. Underfull \hbox (badness 10000) in paragraph at lines 2020--2020 [] \OT1/cmr/bx/n/14.4 Var-i-ous kind-s of con-nect-ed-ness [] [37 ] [38 ] Chapter 3. Underfull \hbox (badness 1655) in paragraph at lines 2054--2061 \OT1/cmr/m/n/10 By a \OT1/cmr/m/it/10 K-naster con-tin-u-um[][] \OT1/cmr/m/n/10 is mean-t a con-tin-u-um home-o-mor-phic to the [] [39] File: ../s/c0003/s0020/e0050/A.eps Graphic file (type eps) <../s/c0003/s0020/e0050/A.eps> File: ../s/c0003/s0020/e0050/B.eps Graphic file (type eps) <../s/c0003/s0020/e0050/B.eps> Overfull \hbox (4.81221pt too wide) has occurred while \output is active \OT1/cmr/m/n/10 40 \OT1/cmr/m/sl/10 CHAPTER 3. DECOMPOSABLE AND INDECOMPOSABL E CONTINUA [] [40] [41] Underfull \hbox (badness 1478) in paragraph at lines 2193--2195 []\OT1/cmr/m/n/10 There is no ex-act-ly 2-to-1 map de-fined on a K-naster con-t in-u-um [] Underfull \hbox (badness 5817) in paragraph at lines 2220--2228 []\OT1/cmr/m/n/10 Moreover, any au-to-home-o-mor-phis-m $\OML/cmm/m/it/10 f$ \O T1/cmr/m/n/10 of a K-naster con-tin-u-um [] Overfull \hbox (4.81221pt too wide) has occurred while \output is active \OT1/cmr/m/n/10 42 \OT1/cmr/m/sl/10 CHAPTER 3. DECOMPOSABLE AND INDECOMPOSABL E CONTINUA [] [42] Underfull \hbox (badness 1264) in paragraph at lines 2244--2248 \OT1/cmr/m/n/10 com-posants of $\OML/cmm/m/it/10 K$\OT1/cmr/m/n/10 , then $\OML /cmm/m/it/10 A$ \OT1/cmr/m/n/10 is mea-ger or comea-ger [[]], [] File: ../s/c0003/s0020/e0050/C.eps Graphic file (type eps) <../s/c0003/s0020/e0050/C.eps> [43] Overfull \hbox (4.81221pt too wide) has occurred while \output is active \OT1/cmr/m/n/10 44 \OT1/cmr/m/sl/10 CHAPTER 3. DECOMPOSABLE AND INDECOMPOSABL E CONTINUA [] [44] Chapter 4. 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COMPACTIFICATIONS OF THE REAL LINE AND THE REAL HALF-LI NE \OT1/cmr/m/n/10 51 [] [51] [52 ] Chapter 5. [53] [54 ] Chapter 6. [55] [56 ] Chapter 7. [57] [58 ] Chapter 8. [59] [60 ] Chapter 9. [61] [62 ] Chapter 10. Underfull \vbox (badness 4927) has occurred while \output is active [] [63] [64] Chapter 11. [65 ] [66 ] Chapter 12. [67] [68 ] Chapter 13. [69] [70 ] Chapter 14. 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[107 ] Underfull \hbox (badness 1881) in paragraph at lines 4018--4032 \OT1/cmr/m/n/10 Given a con-tin-u-um $\OML/cmm/m/it/10 X$ \OT1/cmr/m/n/10 with an arc-structure $\OML/cmm/m/it/10 A$\OT1/cmr/m/n/10 , the pair $(\OML/cmm/m/it /10 X; A\OT1/cmr/m/n/10 )$ (see [] [108] Underfull \hbox (badness 10000) in paragraph at lines 4052--4057 [] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] Underfull \hbox (badness 1817) in paragraph at lines 5157--5160 \OT1/cmr/m/n/10 any t-wo of it-s sub-con-tin-u-a with nonemp-ty in-te-ri-ors is con-nect-ed (see [] [128] [129] [130 ] Appendix B. (ect.ind Underfull \hbox (badness 10000) in paragraph at lines 5207--1 [] [131] [132] [133] [134 ] [135] [136] Underfull \hbox (badness 10000) in paragraph at lines 312--313 []\OT1/cmr/m/n/10 weakly hered-i-tar-i-ly u-ni-co-her-en-t, [] [137 ]) [138 ] [139] [140] Underfull \hbox (badness 3657) in paragraph at lines 5568--5570 []\OT1/cmr/m/n/10 J. J. Chara-tonik and P. Krup-s-ki, \OT1/cmr/m/it/10 On self- [] Underfull \hbox (badness 1953) in paragraph at lines 5572--5575 []\OT1/cmr/m/n/10 W. J. Chara-tonik and A. Dilk-s, \OT1/cmr/m/it/10 On self- [] [141] [142] [143] [144] [145] Underfull \hbox (badness 2426) in paragraph at lines 5897--5900 []\OT1/cmr/m/n/10 P. Pyri-h, \OT1/cmr/m/it/10 An ex-am-ple re-lat-ed to strong- ly point-wise self- [] Underfull \hbox (badness 1297) in paragraph at lines 5911--5913 []\OT1/cmr/m/n/10 J. T. Roger-s, Jr., \OT1/cmr/m/it/10 Map-ping solenoid-s on-t o strong-ly self- [] Underfull \hbox (badness 1205) in paragraph at lines 5943--5945 []\OT1/cmr/m/n/10 K. Siek-luc-k-i, \OT1/cmr/m/it/10 On a fam-i-ly of pow-er $\U /euf/m/n/10 c$ \OT1/cmr/m/it/10 con-sist-ing of $\U/euf/m/n/10 R$\OT1/cmr/m/it/ 10 - [] [146] [147] (ect.aux) LaTeX Warning: There were multiply-defined labels. ) Here is how much of TeX's memory you used: 3026 strings out of 55881 35852 string characters out of 210266 76714 words of memory out of 262143 5374 multiletter control sequences out of 10000 17562 words of font info for 67 fonts, out of 81920 for 254 19 hyphenation exceptions out of 607 27i,14n,24p,497b,484s stack positions out of 300i,100n,60p,5000b,1000s Output written on ect.dvi (147 pages, 303044 bytes).