Geodesic
Product Maps and Countable Paracompactness
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1187-1190

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

In all that follows, we let S denote the space {0, 1, 1/2, ... , 1/n, ...} with the relative usual topology and i : S → S denote the identity map on S. In this note, by a map or mapping we always mean a continuous surjection. A map f : X → Y is said to be hereditarily quotient if y ∊ int f(V) whenever V is open in X and f -1(y) ⊂ V. E. Michael has defined a map f : X → Y to be bi-quotient if whenever is a collection of open sets in X which covers f -1(y), there exists finitely many f(V), with V ∊ , which cover some neighbourhood of y. 
Martin, Harold W. Product Maps and Countable Paracompactness. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1187-1190. doi: 10.4153/CJM-1972-128-7
@article{10_4153_CJM_1972_128_7,
     author = {Martin, Harold W.},
     title = {Product {Maps} and {Countable} {Paracompactness}},
     journal = {Canadian journal of mathematics},
     pages = {1187--1190},
     year = {1972},
     volume = {24},
     number = {6},
     doi = {10.4153/CJM-1972-128-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-128-7/}
}
TY  - JOUR
AU  - Martin, Harold W.
TI  - Product Maps and Countable Paracompactness
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 1187
EP  - 1190
VL  - 24
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-128-7/
DO  - 10.4153/CJM-1972-128-7
ID  - 10_4153_CJM_1972_128_7
ER  - 
%0 Journal Article
%A Martin, Harold W.
%T Product Maps and Countable Paracompactness
%J Canadian journal of mathematics
%D 1972
%P 1187-1190
%V 24
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-128-7/
%R 10.4153/CJM-1972-128-7
%F 10_4153_CJM_1972_128_7

[1] 1. Dowker, C. H., On countably paracompact spaces, Can. J. Math. 3 (1951), 219–224. Google Scholar

[2] 2. Dugundji, J., Topology (Allyn and Bacon, Boston, 1966). Google Scholar

[3] 3. Franklin, S. P., Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–116. Google Scholar

[4] 4. Franklin, S. P., Spaces in which sequence suffice. II, Fund. Math. 61 (1967), 51–56. Google Scholar

[5] 5. Harley, P., On countably paracompact spaces and closed maps (to appear). Google Scholar

[6] 6. Henriksen, M. and Isbell, J. R., Some properties of compactifications, Duke Math. J. 25 (1958), 83–105. Google Scholar

[7] 7. Ishikawa, T., On countably paracompact space, Proc. Japan Acad. 31 (1955), 686–687. Google Scholar

[8] 8. Krajewski, L., On expanding locally finite collections, Can. J. Math. 23 (1971), 58–68. Google Scholar

[9] 9. Michael, E., A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173–176. Google Scholar

[10] 10. Michael, E., Bi-quotient maps and cartesian products of quotient maps, Ann. Inst. Fourier (Grenoble) 18 (1968), 287–302. Google Scholar

[11] 11. Noble, N., Products with closed projections, Trans. Amer. Math. Soc. 160 (1971), 169–183. Google Scholar

[12] 12. Whyburn, G. T., Accessibility spaces, Proc. Amer. Math. Soc. 24 (1970), 181–185. Google Scholar

[13] 13. Zenor, P., On countable paracompactness and normality, Prace Mat. 13 (1969), 23–32. Google Scholar

Cité par Sources :