Institut for Matematiske Fag – Københavns Universitet
Transcript of Institut for Matematiske Fag – Københavns Universitet
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How to control limits in Gedsets
suppose we have a diagram Put
it in sore common K Conant
t Im HttF ToK Snell
If we can guarantee thatHe colin is Idiagramt filteredthen this futarcoundes
with the Unit over the
diagram
Karma let eoflt.cl be the
alinilitality of K
of I at d
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indexed colin of K small
sets is still k small
Clair l Coftkt can bewurde arbitrarily lage
42 Category of Ist
T ITTo E Small IS
off KI filtered
Enough A show a coffktSmart Hurt of Kanal
Haris is k small
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Enough to laut Txic.I
Ikie.LIki zE
i
2 KK
if kj are Kusmell K
RtFirst Gretl Xl D
sheaf
E Condsets
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Clair Hari is exactlythe full subcategory ofaces condensed sets
Pf EH Each object of Hasit go because of the
Anita nahe Nthtpdsy.CH
If X is go it atmet
a Surgeon from a
2 Efta Has SpaceH
ya and coarselyL ly 1 alten
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2 III an gar
4 cm X is
t teX goss scott
of 4
Haineei net nHaus
X
Quali separated contented sets
Hausdorf
Clair A condensed set isquasi separated
it i 4 filter colin ofHaus spaces dafür
y
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iniedremops includesrt Han
PI gap obj dead man
filtered almswliujknns.tnups
X g separated
hat links XKenT
fiteed ans
fke k X
K PinfftGanzeµ
im A am KEK K
f
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g Has
tustratet of
K by a dreiesi d n
c Hus
X im KKt XA
Cart T E
um
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Addudmitbmlyki.fiEICanjtmsitionmrsI
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liefIIHomlki Ki
Sep Card Set
E Ind CH
spanned by those with
injeothetrusrtinmaps
Szene a Walbroke companyspaces
GWH top space11 I
q Up Cab Gets TH Gut
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PI KWH Etat colmöfit Hors
Content X ConttxHaus
als re Cmd at U all CthsSchnees
It's not emshtake zu
Haus subspace filteredunionist X
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EH od filtered aufof Gtaspaces EIN u E 3
b c top is seventh
but the alin is notpresent byGtw G d
OTOH ach tu tut dogpreteen watschle se
Under drug closed Etwasintnide disput omnes
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pusht of Men paswho I my Dan inclusion
7 left adjoint to 7hDrum
g Sep Cordsets
Sep if ahh
X H XSep
Konto built it
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Ki Rr C Chas
HK L
c Kiki
We can just erlogenht takes the smallestclosely earth geredet
btit.TK
Xtam
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prune site products
induce analoges
frites 01Gb Ab Cod Riss
The aber was betHausdorff phenomena
b t it's my importanthat ne hm lots of
Hausdorff phenomenatoo
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EIN ContAbdienteXpysvoltp.IQ1112
in Top ab sps this
nap D both anonomorphbuszu
pimiphrsm.brtlobvieslyInoIaniso
When me pas La andSomething different mist happen
landab Dan ab
at
R
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tma
highly men Hasdorffa dosed Ab gp
EinwIRS AIR Rts
5 non Handoff hat
Maske 0
a underlying setof a and at
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yiii.net.in
4 TI hattettr.deHas zue
Gutan
EE
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12 X top spee
Gatt x
D a sheaf on Haus
When is it a Card Set
i e when is it the can
that Cat Xl isn small colin ofrepresentable 7
Ae E Xii TCall pts are closed
Prof in Rete notes Gedensehpf