On the spectralization of affine and perfectly normal spaces

References

[1] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969. Search in Google Scholar

[2] C. E. Aull and R. Lowen, Handbook of the History of General Topology. Vol. 1, Kluwer Academic, Dordrecht, 1997. 10.1007/978-94-017-0468-7Search in Google Scholar

[3] A. Ayache and O. Echi, The envelope of a subcategory in topology and group theory, Int. J. Math. Math. Sci. 2005 (2005), no. 21, 3387–3404. 10.1155/IJMMS.2005.3387Search in Google Scholar

[4] B. Banaschewski, Coherent frames, Continuous Lattices, Lecture Notes in Math. 871, Springer, Berlin (1981), 1–11. 10.1007/BFb0089900Search in Google Scholar

[5] S. Bloom, Basic theory of algebraic geometry, preprint (2010), http://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Bloom.pdf. Search in Google Scholar

[6] R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann, Berlin, 1989. Search in Google Scholar

[7] L. Gillman and M. Jerison, Rings of Continuous Functions, D. Van Nostrand, Princeton, 1960. 10.1007/978-1-4615-7819-2Search in Google Scholar

[8] J. Goubault-Larrecq, Non-Hausdorff Topology and Domain Theory, New Math. Monogr., Cambridge University Press, Cambridge, 2013. 10.1017/CBO9781139524438Search in Google Scholar

[9] J. Goubault-Larrecq, http://projects.lsv.ens-cachan.fr/topology/?page_id=12. Search in Google Scholar

[10] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977. 10.1007/978-1-4757-3849-0Search in Google Scholar

[11] M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43–60. 10.1090/S0002-9947-1969-0251026-XSearch in Google Scholar

[12] W. Hurewicz and H. Wallman, Dimension Theory, Princeton Math. Ser. 4, Princeton University Press, Princeton, 1941. Search in Google Scholar

[13] P. T. Johnstone, Stone Spaces, Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1986. Search in Google Scholar

[14] V. Kannan, Reflexive cum coreflexive subcategories in topology, Math. Ann. 195 (1972), 168–174. 10.1007/BF01419625Search in Google Scholar

[15] S. MacLane, Categories for the Working Mathematician, Grad. Texts in Math. 5, Springer, New York, 1971. 10.1007/978-1-4612-9839-7Search in Google Scholar

[16] R. G. Montgomery, Structures determined by prime ideals of rings of functions, Trans. Amer. Math. Soc. 147 (1970), 367–380. 10.1090/S0002-9947-1970-0256174-4Search in Google Scholar

[17] R. G. Montgomery, The mapping of prime z-ideals, Symposia Mathematica. Vol. XVII (Rome 1973), Academic Press, London (1976), 113–124. Search in Google Scholar

[18] N. Schwartz, Locales as spectral spaces, Algebra Universalis 70 (2013), no. 1, 1–42. 10.1007/s00012-013-0241-4Search in Google Scholar

[19] N. Schwartz, Spectral reflections of topological spaces, Appl. Categ. Structures 25 (2017), no. 6, 1159–1185. 10.1007/s10485-017-9488-9Search in Google Scholar

[20] J. Schröder, Das Wallman-Verfahren und inverse Limites, Quaest. Math. 2 (1977/78), no. 1–3, 325–333. 10.1080/16073606.1977.9632552Search in Google Scholar

[21] A. Tarizadeh, On the category of profinite spaces as a reflective subcategory, Appl. Gen. Topol. 14 (2013), no. 2, 147–157. 10.4995/agt.2013.1575Search in Google Scholar

[22] The Stacks Project, https://stacks.math.columbia.edu/tag/08YF. Search in Google Scholar