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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Topological representation of lattice homomorphism
s - Blaszczyk\, A (University of Silesia in Katowi
ce)
DTSTART;TZID=Europe/London:20150824T140000
DTEND;TZID=Europe/London:20150824T143000
UID:TALK60432AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60432
DESCRIPTION:Wallman proved that if $mathbb{L}$ is a distributi
ve lattice with $mathbf{0}$ and $mathbf{1}$\, the
n there is a $T_1$-space with a base (for closed s
ubsets) being a homomorphic image of $mathbb{L}$.
We show that this theorem can be extended over h
omomorphisms. More precisely: if $f{Lat}$ denotes
the category of normal and distributive lattices
with $mathbf{0}$ and $mathbf{1}$ and homomorphisms
\, and $f{Comp}$ denotes the category of compact
Hausdorff spaces and continuous mappings\, th
en there exists a contravariant functor $mathcal{
W}:f{Lat} of{Comp}$. When restricted to the subc
ategory of Boolean lattices this functor coincides
with a well-known Stone functor which realizes th
e Stone Duality. The functor $mathcal{W}$ carries
monomorphisms into surjections.\n However\, it do
es not carry epimorphisms into injections.\n The l
ast property makes a difference with the Stone f
unctor.\n Some applications to topological constru
ctions are given as well.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:
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