Geodesic
Symmetrizable, -, and Weakly First Countable Spaces
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 480-488

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

A number of results are given concerning the character and cardinality of symmetrizable and related spaces. An example is given of a symmetrizable Hausdorff space containing a point that is not a regular Gδ , and a proof is given that if a point p of a symmetrizable Hausdorff space has a neighborhood base of cardinality , then p is a Gδ . It is shown that for each cardinal number m there exists a locally compact, pseudocompact, Hausdorff -space X with |X| ≧ m. Several questions of A. V. Arhangel'skii and E. Michael are partially answered. 
Stephenson, R. M. Symmetrizable, -, and Weakly First Countable Spaces. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 480-488. doi: 10.4153/CJM-1977-052-4
@article{10_4153_CJM_1977_052_4,
     author = {Stephenson, R. M.},
     title = {Symmetrizable, -, and {Weakly} {First} {Countable} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {480--488},
     year = {1977},
     volume = {29},
     number = {3},
     doi = {10.4153/CJM-1977-052-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-052-4/}
}
TY  - JOUR
AU  - Stephenson, R. M.
TI  - Symmetrizable, -, and Weakly First Countable Spaces
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 480
EP  - 488
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-052-4/
DO  - 10.4153/CJM-1977-052-4
ID  - 10_4153_CJM_1977_052_4
ER  - 
%0 Journal Article
%A Stephenson, R. M.
%T Symmetrizable, -, and Weakly First Countable Spaces
%J Canadian journal of mathematics
%D 1977
%P 480-488
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-052-4/
%R 10.4153/CJM-1977-052-4
%F 10_4153_CJM_1977_052_4

[1] 1. Arhangel'skii, A. V., Mappings and spaces, Uspehi Mat. Nauk 21 (1966), no. 4 ﹛130), 133-184 Russian Math. Surveys 21 (1966), no. 4, 115–162. Google Scholar

[2] 2. Arhangel'skii, A. V. On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl 10 (1969), 951–955. Google Scholar

[3] 3. Bonnett, D. A., A symmetrizable space that is not perfect, Proc. Amer. Math. Soc. 34 (1972), 560–564. Google Scholar

[4] 4. Franklin, S. P., Spaces in which sequences suffice, II, Fund. Math. 57 (1967), 51–56. Google Scholar

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

[6] 6. Harley, Peter W., III and Stephenson, R. M., Jr., Symmetrizable and related spaces, Trans. Amer. Math. Soc. 217 (1976), to appear. Google Scholar

[7] 7. Nedev, S., Symmetrizable spaces and final compactness, Soviet Math. Dokl. 8 (1967), 890–892. Google Scholar

Cité par Sources :