Set A
well
. lulian
on dishimed bjej
Celul a t wte Ay "well dafd" w
ut b a ule 01 Ales
wtiudv thnld erdily be aleo
Ay wfilw a paadituulan djet a memh
enbe set.
: XxXR at sutispisd folloig nalitiong
l(, ) 2o fr all *,y éX
o,)
A, )(7,) tr all y€X
A(L) < «(1, )+ A(1,2) all ,EX
fr
os a on a se X, nadertd pa
(x,) Caller mnic ane
l,
ziakteperla: Tpolayiul prpetu
whic L nsrrd uei hemtomrplims ie bijui
biudinss (-m, endo, A,p )
eerivndeaw k reds,
Topos aud logos . Tp htanin 4urfaue al
.
suly Tpelegy Liually
mtanin olisuru mand
sues Aiee ooriden Ttolay
O,
shuly folzind peputiu"
kounen nnudeulns an paten
Spasin, alU
aAdpoto gha uiay . wkAe angle , tAmplidenu,
oli'stn , Brdul ndtdsjint uopei
1p Felix ollsl
Hauselon bb shut miuy
gims
a asstded ida pegy1/
Scanned with CamScanner
ETEATNHN YT
,saeaA dpolil an (x,T)
Caisi a aaidy T ubub f X
4a4. aet X
4niemd
fotlog
xeT a menbe
Co,1
Abiimay nio mhau T4
LThe
T
ft ilinetins nbus T4 a
&T. spare ad ih lemnt
The se X alA a
dfind a
alll rins dh at: Tau
Hmben
T y nlbd
dopolgial ue (xT) ad
se opoteay en X.
h
Ca be stabl tlenws
ukee sdl x at opes ut.
(4T npty ut ad many opes suli ohn t
Th uniom sbiuy
u a puil trpogial
Erasn A aLt
op
a
t hae (x, 4) a4L
aX
Ary
(X,4)
p
Thuns etegj lled
Vyual dspalrgy
Esame 2kt X be any w a T {, x3. Toraly
all he Anios ( d ta).Thus T dei
T 4atis
X And nllen insdis uuke solegs
ivial aerlogy
Scanned with CamScanner
, Pags do 3
. fai a
any ut ad T b he
S e3 X
T defints
all 4ubeh X 4.e T e(x). Thew
apology ulted isuci trprlaj
otosn Ty
tlleulion odubus d X nt
X. AML dh ay
ansd elisuile deln
fane tinak tpolty
dopoagia
t semi
T:},x, fa35
{,33
4,x,
T
,1à33
T
4,
, ,
4,x,
*,
X, sa3,
(a,å), 14,}
{, fakj}{,63, {1,3)
s«, s3,
at au roi
dopotogis
olttions dubrk X
aL
{%<3f, },X, fa,i3j
,x, X
1,1,
bu ay dubk x.
Erame5t mpleenk k
(sien]
ET T
famiy mbrs
eidh O o X-0 nide
lsydnay
i.t
(x-0):
X ot fie
X-Y
T
O
Scanned with CamScanner
, But 0e eT,
. X-04 fik 4 Is isn
sut 1
T
fmand tiike
ThuTr s A trpolegy m ,
bo te x e a tinit set and T be inik yY
uk be ay ubsut 1 X.
E X-x-E) al x-t) $ nik f: X fnik)
EE T ie T is eete depeg
and T be h
x hu av unurutable sut
Examhkenb tet anal all tmplimenty
4ubser X mdiy
X, Th T s
osuhte alledo-Cuusesad subzek a kopeeay en X
Ael
Souion Co
ad
eT (in)
X ,
s4 ntahke XeT
nbinmy membeu T.
X-O uabke
X
nminble
-O By e Moya dhena
X-yo n(x-0)
X ntuhe
Thay 0
OT ay i fo:3 be
nanbtas T.
t
e x-o (x-)
aaw oz ff * Isi
tt
Scanned with CamScanner
well
. lulian
on dishimed bjej
Celul a t wte Ay "well dafd" w
ut b a ule 01 Ales
wtiudv thnld erdily be aleo
Ay wfilw a paadituulan djet a memh
enbe set.
: XxXR at sutispisd folloig nalitiong
l(, ) 2o fr all *,y éX
o,)
A, )(7,) tr all y€X
A(L) < «(1, )+ A(1,2) all ,EX
fr
os a on a se X, nadertd pa
(x,) Caller mnic ane
l,
ziakteperla: Tpolayiul prpetu
whic L nsrrd uei hemtomrplims ie bijui
biudinss (-m, endo, A,p )
eerivndeaw k reds,
Topos aud logos . Tp htanin 4urfaue al
.
suly Tpelegy Liually
mtanin olisuru mand
sues Aiee ooriden Ttolay
O,
shuly folzind peputiu"
kounen nnudeulns an paten
Spasin, alU
aAdpoto gha uiay . wkAe angle , tAmplidenu,
oli'stn , Brdul ndtdsjint uopei
1p Felix ollsl
Hauselon bb shut miuy
gims
a asstded ida pegy1/
Scanned with CamScanner
ETEATNHN YT
,saeaA dpolil an (x,T)
Caisi a aaidy T ubub f X
4a4. aet X
4niemd
fotlog
xeT a menbe
Co,1
Abiimay nio mhau T4
LThe
T
ft ilinetins nbus T4 a
&T. spare ad ih lemnt
The se X alA a
dfind a
alll rins dh at: Tau
Hmben
T y nlbd
dopolgial ue (xT) ad
se opoteay en X.
h
Ca be stabl tlenws
ukee sdl x at opes ut.
(4T npty ut ad many opes suli ohn t
Th uniom sbiuy
u a puil trpogial
Erasn A aLt
op
a
t hae (x, 4) a4L
aX
Ary
(X,4)
p
Thuns etegj lled
Vyual dspalrgy
Esame 2kt X be any w a T {, x3. Toraly
all he Anios ( d ta).Thus T dei
T 4atis
X And nllen insdis uuke solegs
ivial aerlogy
Scanned with CamScanner
, Pags do 3
. fai a
any ut ad T b he
S e3 X
T defints
all 4ubeh X 4.e T e(x). Thew
apology ulted isuci trprlaj
otosn Ty
tlleulion odubus d X nt
X. AML dh ay
ansd elisuile deln
fane tinak tpolty
dopoagia
t semi
T:},x, fa35
{,33
4,x,
T
,1à33
T
4,
, ,
4,x,
*,
X, sa3,
(a,å), 14,}
{, fakj}{,63, {1,3)
s«, s3,
at au roi
dopotogis
olttions dubrk X
aL
{%<3f, },X, fa,i3j
,x, X
1,1,
bu ay dubk x.
Erame5t mpleenk k
(sien]
ET T
famiy mbrs
eidh O o X-0 nide
lsydnay
i.t
(x-0):
X ot fie
X-Y
T
O
Scanned with CamScanner
, But 0e eT,
. X-04 fik 4 Is isn
sut 1
T
fmand tiike
ThuTr s A trpolegy m ,
bo te x e a tinit set and T be inik yY
uk be ay ubsut 1 X.
E X-x-E) al x-t) $ nik f: X fnik)
EE T ie T is eete depeg
and T be h
x hu av unurutable sut
Examhkenb tet anal all tmplimenty
4ubser X mdiy
X, Th T s
osuhte alledo-Cuusesad subzek a kopeeay en X
Ael
Souion Co
ad
eT (in)
X ,
s4 ntahke XeT
nbinmy membeu T.
X-O uabke
X
nminble
-O By e Moya dhena
X-yo n(x-0)
X ntuhe
Thay 0
OT ay i fo:3 be
nanbtas T.
t
e x-o (x-)
aaw oz ff * Isi
tt
Scanned with CamScanner
