A Kuratowski theorem for some pseudosurfaces
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3$ d qY `jjkhRYR RZPs{ O z 1 $t$8sj tBtT8AIsAj Ps8$j$R PB z & " , - ! n qYB8 d N A s s}Y b$Y s jsR Y %${R $R st 8AIsAj s}Y PB n $P stI Btjk $P YsR bB }jsts RZAs}YR d stI 1 RB Ys d 1 & \ d 1 n i stI d 1 & bY 7 ; PB & " % . , ]BBjjsk 1 z sI8$R st 8AII$t $t n PB ; / wR 3$Z 1D 43
J J J J I I J J I I I I H H H H z 1 z O 1 O n 44 ) ) &&& & MMM Z Z Z Z)))*** *** <<< < c c c c c c 44 ) ) &&& & MMM Z Z Z Z))) *** *** <<< < c c c c c c c c / ! ! z " # 1 z $ " 1 z n / ! " & 0" z x E ; / & z x E ; / ,+ 1 z !! ; & 0 " 1 z x !! ! E ; / / 1 , z " 2 ; / !! z ' 1 ( ! 1 " , # # ' 1 ( $ 1 ! ) 1 \ x n , n i ! ) 3 44
d 1 n d 1 n d 1 n d 1 n n % 7 )d I 7 I d < ` I 1 < 8 I n w I d < I 1 D I n n 7 )d I 7 3$ ; $t$8sj tBt 1T{Btt{I PBA$IIt 8$tBR qB }B% BZ 8s$t YB8 b I$R$tZ$RY 1T{Btt{I stI tBt 1T{Btt{I PBA$IIt s}YR qY PBjjBb$t RZj RYBbR Y 8$t$8sj 1T{Btt{I tBtT 8AIsAj s}YR qYB8 N ? A s y_ 1 w yi DT7 1 T{jjZjs PBR b$Y s jsR Bt }B`{$% }jst sR s {jj t $R s 8$t$8sj 1T{Btt{I tBtT8AIsAj s}YR $t ? $P stI Btjk $P t $R s 8$t$8sj 1T{Btt{I tBtT8AIsAj s}YR $t y_ 1 w yi D WB${ Ys tB sjj BARZ{$Bt RR BP y_ 1 wyiDT7 1 T{jjZjs PBRR {st A BAT s$tI ZR$t Y c 1 BI 3B $tRst{ x n x sI8$R st 8AII$t $tB y_ 1 wyiD ` 7 1 ` y_ 1 wyiD stI x ` x IBR tB <Bb% x ` x c 1 x n x Vy_ 1 w yi D T7 1 T{jjZjs PBR YsR st BARZ{$Bt R R}{ Y c 1 BI $P stI Btjk $P s{Y {Btt{I {B8}Btt YsR s 8BR Bt R$tZjs }B$t qY R BP Y 8$t$8sj tBt 1T{Btt{I PBA$IIt s}YR I}tIR Bt Y }s${Zjs y_ 1 w yi D T7 1 T{jjZjs PBR <Bb% Yk sjj {Bts$t Y Rs8 ,$tI BP AjB{,R w R 3$Z n D VR st -s8}j tB${ Ys x x $R s 8$t$8sj tBtT8AIsAj s}Y PB y_ 1 wyiD ` 7 1 ` 7 1 ` y_ 1 wyiD stI x n x $R s 8$t$8sj tBtT8AIsAj s}Y PB y_ 1 wyiD y_ 1 wyiD ABY PB Y c d BI 3$tsjjk sR s }s${Zjs {sR Y PBjjBb$t RZj RsR Y 8$t$8sj tBt 1T {Btt{I PBA$IIt 8$tBR PB bB y_ 1 wyiDT7 1 T{jjZjs PBRRU y_ 1 wyiD y_ 1 wyiD stI y_ 1 wyiD ` y_ 1 wyiD wR 3$Z ;D qYB8 M qY PBjjBb$t Rs8tR s %$hI wdD qY 8$t$8sj tBt 1T{Btt{I PBA$IIt 8$tBR PB y_ 1 w yi D y_ 1 w yi Ds \ I d ` I 1 i l n 7 )d I 7 M bY I 7 ;\ x , n , n i PB 7 )d , 1 , n w1D qY 8$t$8sj tBt 1T{Btt{I PBA$IIt 8$tBR PB y_ 1 w yi D ` y_ 1 w yi Ds \ w I d ` I 1 D I n i l n 7 )d I 7 M l n % 7 )d I 7 M \ I d ` ` I 1 ` 8 I n i bY I 7 ; \ x , n , n i PB 7 )d , 1 , n VR s {BtRJZt{ y_ 1 wyiD ` y_ 1 wyiD YsR ; 8$t$8sj PBA$IIt 8$tBR stI y_ 1 wyiD y_ 1 wyiD YsR nE BtR 45
>dH * V{YIs{Bt V ZsBbR,$ qYB8 PB Y _B`{$% _jst FBZtsj BP ps}Y qYBk xU1;nu1;E dMd >1H BItI$, stI Gst 7BjZ$Bt B [Bt$:R s}Y 8AII$t }BAj8 sY Ws{Y d;(U1xdu11 dM >nH < < pjB% F _ <Zt, stI ] 7 Gst d(n s}YR Ys s $IZ{$Aj PB Y }B`{$% }jst FBZtsj BP ]B8A$tsB$sj qYBk 1 w n D Unn1un( d >;H 3 <ssk ps}Y qYBk VII$RBt GRjk isI$t sRR dE >xH ZsBbR,$ 7Z j }BAjr8 IR {BZAR sZ{YR t B}BjB$ 3ZtI sY dxU1du1Mn dn( >EH W iBARBt stI _ * 7k8BZ ps}Y $tBR zyyy V ZsBR,$ qYB8 PB ptsj 7ZPs{R F ]B8A$tsB$sj qYBk 7$ ;MU1xxu1MM d( >H F 6 7$?s6t stI _ p%B9I`s, ZsBbR,$Tqk} qYB8R *B WB e-tI B _RZIBRZPs{R F {B8A$tsB$sj qY Bk 7 x;U1(u1d1 d1 46