COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Topological representation of lattice homomorphisms

## Topological representation of lattice homomorphismsAdd to your list(s) Download to your calendar using vCal - Blaszczyk, A (University of Silesia in Katowice)
- Monday 24 August 2015, 14:00-14:30
- Seminar Room 2, Newton Institute Gatehouse.
If you have a question about this talk, please contact webseminars. Mathematical, Foundational and Computational Aspects of the Higher Infinite Wallman proved that if $mathbb{L}$ is a distributive lattice with $mathbf{0}$ 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 that this theorem can be extended over homomorphisms. 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, then there exists a contravariant functor $mathcal{W}:f{Lat} of{Comp}$. When restricted to the subcategory of Boolean lattices this functor coincides with a well-known Stone functor which realizes the Stone Duality. The functor $mathcal{W}$ carries monomorphisms into surjections. However, it does not carry epimorphisms into injections. The last property makes a difference with the Stone functor. Some applications to topological constructions are given as well. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 2, Newton Institute Gatehouse
- bld31
Note that ex-directory lists are not shown. |
## Other listsMathematics of John Thompson Conference on Finite Groups and related topics Biotech Talks- Dept of Biochemistry Festival of Ideas: Spotlight Talks## Other talksNo interpretation of probability Is Demand Side Response a woman’s work? Gender dynamics in a field trial of smart meters and Time of Use tariffs in east London. Migration in Science Chemical genetic approaches to accelerate antimalarial target discovery Current-Induced Stresses in Ceramic Lithium-Ion Conductors ‘Class-work’ in the elite institutions of higher education |