Geodesic
Some Properties of θ-Closure
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 142-149

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

The concept of θ-closure was introduced by Velicko to study H-closed spaces and to generalize Taimanov's extension theorem [11], [12]. More recently, this notion has been used by Dickman and Porter [1] to characterize those Hausdorff spaces in which the Fomin H-closed extension operator commutes with the projective cover (absolute) operator and [2] to study extentions of functions. If X is a topological space and A ⊂ X, we let Σ(A) and Γ(A) represent, respectively, the family of open subsets which contain A and closed subsets which contain some element of Σ(A). The θ-closure of A ⊂ X, denoted by clθ (A) (clθ (v) if A = {v}), is {x ∈ X: each V ∈ Γ(x) satisfies V ∩ A ≠ ∅} and A is called θ-closed in case clθ (A) = A. 
Espelie, M. Solveig; Joseph, James E. Some Properties of θ-Closure. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 142-149. doi: 10.4153/CJM-1981-013-8
@article{10_4153_CJM_1981_013_8,
     author = {Espelie, M. Solveig and Joseph, James E.},
     title = {Some {Properties} of {\ensuremath{\theta}-Closure}},
     journal = {Canadian journal of mathematics},
     pages = {142--149},
     year = {1981},
     volume = {33},
     number = {1},
     doi = {10.4153/CJM-1981-013-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-013-8/}
}
TY  - JOUR
AU  - Espelie, M. Solveig
AU  - Joseph, James E.
TI  - Some Properties of θ-Closure
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 142
EP  - 149
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-013-8/
DO  - 10.4153/CJM-1981-013-8
ID  - 10_4153_CJM_1981_013_8
ER  - 
%0 Journal Article
%A Espelie, M. Solveig
%A Joseph, James E.
%T Some Properties of θ-Closure
%J Canadian journal of mathematics
%D 1981
%P 142-149
%V 33
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-013-8/
%R 10.4153/CJM-1981-013-8
%F 10_4153_CJM_1981_013_8

[1] 1. Dickman, R. F. and Porter, J. R., 6–closed subsets of Hausdorff spaces, Pacific J. Math. 59 (1975), 407–415. Google Scholar

[2] 2. Dickman, R. F. and Porter, J. R., θ-perfect and θ–absolutely closed functions, Illinois J. Math. 21 (1977), 42–60. Google Scholar

[3] 3. Fomin, S., Extensions of topological spaces, Ann. Math. 44 (1943), 471–480. Google Scholar

[4] 4. Herrington, L. L., H(i) spaces and strongly-closed graphs, Proc. Amer. Math. Soc 58 (1976), 277–283. Google Scholar

[5] 5. Joseph, J. E., θ-closure and θ–subclosed graphs, Math. Chron. 8 (1979), 99–117. Google Scholar

[6] 6. Joseph, J. E., Multifunction and cluster sets, Proc. Amer. Math. Soc. 74 (1979), 329–337. Google Scholar

[7] 7. Joseph, J. E., Multifunctions and graphs, Pacific J. Math. 79 (1978), 509–529. Google Scholar

[8] 8. Porter, J. and Thomas, J., On H-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138 (1969), 159–170. Google Scholar

[9] 9. Smithson, R. E., Multifunctions, Nieuw Archief voor Wiskunde 20 (1972), 31–53. Google Scholar

[10] 10. Thompson, T., Concerning certain subsets of non-Hausdorff topological spaces, Boll. U.M.I. 14–A (1977), 34–37. Google Scholar

[11] 11. Velicko, N. V., H-closed topological spaces, Mat. Sb. 70 (112) (1966), 98–112; Amer. Math. Lee. Transi. 78 (Series 2) (1969), 103–118. Google Scholar

[12] 12. Velicko, N. V., On the theory of H-closed topological spaces, Sibirskii Mat. Z. 8 (1967), 754– 763; Translation: Siberian Math. J. 8 (1967), 569–579. Google Scholar

Cité par Sources :