Geodesic
On the Lattice of Primitive Convergence Structures
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 392-397

Voir la notice de l'article provenant de la source Cambridge University Press

Let S be any set and denote by F(S) the collection of all fiters on S. The collection A(S) of all mappings from F(S) to 2s , 2s being ordered by the dual of its usual ordering, may be regarded as a product of complete Boolean algebras and is, therefore, a complete atomic Boolean algebra [4]. A(S) is called the lattice of primitive convergence structures on S. If q ∈ A(S) and , then is said to q-converge to a point x ∈ S if . The collection of all topologies on S may be identified with a subset of A(S); this subset of A(S) will be denoted by T(S). A more specialized class of primitive convergence structures, and one which properly contains T(S), is C(S), the subcomplete lattice of all convergence structures on S. 
Jr., C. R. Atherton. On the Lattice of Primitive Convergence Structures. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 392-397. doi: 10.4153/CJM-1971-040-0
@article{10_4153_CJM_1971_040_0,
     author = {Jr., C. R. Atherton},
     title = {On the {Lattice} of {Primitive} {Convergence} {Structures}},
     journal = {Canadian journal of mathematics},
     pages = {392--397},
     year = {1971},
     volume = {23},
     number = {3},
     doi = {10.4153/CJM-1971-040-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-040-0/}
}
TY  - JOUR
AU  - Jr., C. R. Atherton
TI  - On the Lattice of Primitive Convergence Structures
JO  - Canadian journal of mathematics
PY  - 1971
SP  - 392
EP  - 397
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-040-0/
DO  - 10.4153/CJM-1971-040-0
ID  - 10_4153_CJM_1971_040_0
ER  - 
%0 Journal Article
%A Jr., C. R. Atherton
%T On the Lattice of Primitive Convergence Structures
%J Canadian journal of mathematics
%D 1971
%P 392-397
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-040-0/
%R 10.4153/CJM-1971-040-0
%F 10_4153_CJM_1971_040_0

[1] 1. Atherton, C. R., Concerning intrinsic topologies on Boolean algebras and certain bicompactly generated lattices, Glasgow Math. J. 11 (1970), 156–161. Google Scholar

[2] 2. Biesterfeldt, H. J., Jr., Completion of a class of uniform convergence spaces, Nederl. Akad. Wetensch. Proc. Ser. A 69 = Indag. Math. 28 (1966), 602–604. Google Scholar

[3] 3. Biesterfeldt, H. J., Jr., Regular convergence spaces, Nederl. Akad. Wetensch. Proc. Ser. A 69 = Indag. Math. 28 (1966), 605–607. Google Scholar

[4] 4. Birkhoff, G., Lattice theory, Third edition, Amer. Math. Soc. Colloq. Publ., Vol. 25 (Amer. Math. Soc, Providence, R. L, 1967). Google Scholar

[5] 5. Choquet, G., Convergences, Ann. Univ. Grenoble Sect. Sci. Math. Phys. (N. S.) 28 (1948), 57–112. Google Scholar

[6] 6. Cook, C. H. and Fischer, H. R., Regular convergence spaces, Math. Ann. 174 (1967), 1–7. Google Scholar

[7] 7. Fischer, H. R., Limesraume, Math. Ann. 137 (1959), 269–303. Google Scholar

[8] 8. Frink, O., Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954), 223–233. Google Scholar

[9] 9. Hearsey, B., On extending regularity and other topological properties to convergence structures, Unpublished Ph.D. dissertation, Washington State University, Pullman, Washington, 1968. Google Scholar

[10] 10. Kent, D. C., Convergence functions and their related topologies, Fund. Math. 54 (1964), 125–133. Google Scholar

Cité par Sources :