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SUMMARY:Topological representation of lattice homomorphisms - Blaszczyk\, 
 A (University of Silesia in Katowice)
DTSTART:20150824T130000Z
DTEND:20150824T133000Z
UID:TALK60432@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Wallman proved that if $mathbb{L}$ is a distributive lattice w
 ith $mathbf{0}$ and  $mathbf{1}$\, then there is a $T_1$-space with a base
  (for closed subsets) being a homomorphic image of $mathbb{L}$. We show th
 at this theorem can be extended   over homomorphisms. More precisely: if $
 f{Lat}$ denotes the category of normal and distributive lattices with $ma
 thbf{0}$ and $mathbf{1}$ and homomorphisms\, and $f{Comp}$  denotes the c
 ategory of compact Hausdorff spaces and continuous mappings\,     then the
 re exists  a contravariant functor $mathcal{W}:f{Lat}	of{Comp}$. When re
 stricted to the subcategory of Boolean lattices this functor coincides wit
 h a well-known Stone functor which realizes the Stone Duality. The functor
  $mathcal{W}$ carries monomorphisms into surjections.\n  However\, it does
  not carry epimorphisms into injections.\n The last property makes a diffe
 rence with the   Stone functor.\n Some applications to topological constru
 ctions are given as well.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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