Geodesic
Spaces in Which Special Sets are z-Embedded
Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 673-690

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

A subset S of a topological space X is z-embedded in X in case each zero-set of S is the restriction to S of a zero-set of X. (A zero-set is the set of zeros of a real-valued continuous function.) For the basic theory of z-embedding, see [3] and [4] (and see [4] for a comprehensive bibliography of relevant papers). 
Blair, Robert L. Spaces in Which Special Sets are z-Embedded. Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 673-690. doi: 10.4153/CJM-1976-068-9
@article{10_4153_CJM_1976_068_9,
     author = {Blair, Robert L.},
     title = {Spaces in {Which} {Special} {Sets} are {z-Embedded}},
     journal = {Canadian journal of mathematics},
     pages = {673--690},
     year = {1976},
     volume = {28},
     number = {4},
     doi = {10.4153/CJM-1976-068-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-068-9/}
}
TY  - JOUR
AU  - Blair, Robert L.
TI  - Spaces in Which Special Sets are z-Embedded
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 673
EP  - 690
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-068-9/
DO  - 10.4153/CJM-1976-068-9
ID  - 10_4153_CJM_1976_068_9
ER  - 
%0 Journal Article
%A Blair, Robert L.
%T Spaces in Which Special Sets are z-Embedded
%J Canadian journal of mathematics
%D 1976
%P 673-690
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-068-9/
%R 10.4153/CJM-1976-068-9
%F 10_4153_CJM_1976_068_9

[1] 1. Blair, R. L., On a theorem of I shell concerning extremally disconnected P-spaces, Arch. Math. 12 (1961), 434. Google Scholar

[2] 2. Blair, R. L., On v-embedded sets in topological spaces, TOPO 72—General Topology and its Applications (Second Pittsburgh International Conference, December 18-22, 1972), Lecture Notes in Math., Vol. 378 (Springer-Verlag, Berlin-Heidelberg-New York, 1974), pp. 46–79. Google Scholar

[3] 3. Blair, R. L., Filter characterizations of s-, C*-, and C-embeddings, Fund. Math. 90 (1976), 285–300. Google Scholar

[4] 4. Blair, R. L. and Hager, A. W., Extensions of zero-sets and of real-valued functions, Math. Zeit. 136 (1974), 41–52. Google Scholar

[5] 5. Blair, R. L. and Hager, A. W., Notes on the Hewitt realcompactification of a product, Gen. Top. Appl. 5 (1975), 1–8. Google Scholar

[6] 6. Blair, R. L. and Hager, A. W., z-embedding in (3X X (3 Y, to appear. Google Scholar

[7] 7. Bourbaki, N., Elements of mathematics: General topology (Hermann, Paris; Addison-Wesley, Reading, Mass., 1966). Google Scholar

[8] 8. Corson, H. H., Normality in subsets of product spaces, Amer. J. Math. 81 (1959), 785–796. Google Scholar

[9] 9. Engelking, R., Outline of general topology (PWN, Warsaw, 1965; English transi., North- Holland, Amsterdam; Interscience, New York, 1968). Google Scholar

[10] 10. Fine, N. J. and Gillman, L., Extension of continuous functions in /3N, Bull. Amer. Math. Soc. 66 (1960), 376–381. Google Scholar

[11] 11. Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, Princeton, 1960). Google Scholar

[12] 12. Hager, A. V., Reynolds, G. D., and Rice, M. D., B or el-complete topological spaces, Fund. Math. 75 (1972), 135–143. Google Scholar

[13] 13. Henriksen, M. and Johnson, D. G., On the structure of a class of archimedean lattice-ordered algebras, Fund. Math. 50 (1961), 73–94. Google Scholar

[14] 14. Isbell, J. R., Zero-dimensional spaces, Tôhoku Math. J., Ser. II 7 (1955), 1–8. Google Scholar

[15] 15. Katétov, M., Measures in fully normal spaces, Fund. Math. 38 (1951), 73–84. Google Scholar

[16] 16. Kelley, J. L., General topology (Van Nostrand, New York, 1955). Google Scholar

[17] 17. Levy, R. F., Almost-F-spaces and Lu sin s hypothesis, Notices Amer. Math. Soc. 22 (1975), A-582. Google Scholar

[18] 18. Mack, J. E. and Johnson, D. G., The Dedekind completion of C(X), Pacific J. Math. 20 (1967), 231–243. Google Scholar

[19] 19. McArthur, V. G., Hewitt realcompactifications of products, Can. J. Math. 22 (1970), 645–655. Google Scholar

[20] 20. Mrowka, S., Some properties of Q-spaces, Bull. Acad. Polon. Sci. CI. I l l 5 (1957), 947–950. Google Scholar

[21] 21. Mrowka, S., On the unions of Q-spaces, Bull. Acad. Polon. Sci. CI. I l l 6 (1958), 365–368. Google Scholar

[22] 22. Mrowka, S., Some comments on the author's example of a non-S?-compact space, Bull. Acad. Polon. Sci. Ser. Math. Astronom. Phys. 18 (1970), 443–448. Google Scholar

[23] 23. Noble, N., C-embedded subsets of products, Proc. Amer. Math. Soc. 31 (1972), 613–614. Google Scholar

[24] 24. Noble, N. and Ulmer, M., Factoring functions on cartesian products, Trans. Amer. Math. Soc. 163 (1972), 329–339. Google Scholar

[25] 25. Ostaszewski, A. J., On countably compact, perfectly normal spaces, J. London Math. Soc, to appear. Google Scholar

[26] 26. Ross, K. A. and Stone, A. H., Products of separable metric spaces, Amer. Math. Monthly 71 (1964), 398–403. Google Scholar

[27] 27. Smirnov, Yu. M., On normally disposed sets of normal spaces, Mat. Sb. (N. S.) 29 (1951), 173–176. (Russian) Google Scholar

[28] 28. Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977–982. Google Scholar

[29] 29. Tamano, H., A note on the pseudocompactness of the product of two spaces, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 225–230. Google Scholar

[30] 30. Tamano, H., On compactifications, J. Math. Kyoto Univ. 1-2 (1962), 161–193. Google Scholar

[31] 31. Veksler, A. I., P'-points, P'-sets, P'-spaces. A new class of order-continuous measures and functional Dokl. Akad. Nauk SSSR 212 (1973), 789-792; Soviet Math. Dokl. 14 (1973), 1445–1450. Google Scholar

[32] 32. Weiss, W. A. R., Some applications of set theory to topology, Ph.D thesis, University of Toronto, 1975. Google Scholar

[33] 33. Willard, S., General topology (Addison Wesley, Reading, Mass., 1970). Google Scholar

Cité par Sources :