# Gelfand spectra and Wallman compactifications

@article{Caramello2012GelfandSA, title={Gelfand spectra and Wallman compactifications}, author={Olivia Caramello}, journal={arXiv: Category Theory}, year={2012} }

We carry out a systematic, topos-theoretically inspired, investigation of Wallman compactifications with a particular emphasis on their relations with Gelfand spectra and Stone-Cech compactifications. In addition to proving several specific results about Wallman bases and maximal spectra of distributive lattices, we establish a general framework for functorializing the representation of a topological space as the maximal spectrum of a Wallman base for it, which allows to generate different…

## 2 Citations

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- Mathematics
- 2018

ing these two fundamental ingredients in the construction of categories of sheaves is precisely what led Grothendieck to introduce the notion of site reviewed in the last section. Sheaves on a…

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