No submaximal topology on a countable set is t1-complementary

Proceedings of the American Mathematical Society

Volumn 128, Issue 1, 2000, Pages 287-297

  Tkačenko, Mikhail G ^a,c   Tkachuk, Vladimir V ^a,b   Wilson, Richard G ^a,b   Yaschenko, Ivan V ^a,b  

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^c Moscow Center for Continuous Mathematical Education   (Russian Federation)

Author keywords

Connected space; Strongly discrete space; Transversal topology

Indexed keywords

EID: 22844455316     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04984-9     Document Type: Article

References (11)

1. 1-complements, Pundamenta Mathematicae, 1970, vol. 69, 267-277. MR 43:6859
2. 1 topologies, Proceedings of the Amer. Math. Soc., 1969, vol. 23, 77-81. MR 39:6240
3. [Ar] A.V.Arhangel'skii, Continuous mappings, factorization theorems and function spaces (in Russian), Trudy Mosk. Mat. Obsch., 1984, vol. 47, 3-21. MR 86i:54002
4. [ArCo] A.V. Arhangel'skii and P.J. Collins, On submaximal spaces, Topology and Its Applications, 1995, vol. 64, no. 3, 219-241. MR 96m:54002
5. [vD] E.K.van Douwen, Applications of maximal topologies, Topology and Its Applications, 1993, vol. 51, 125-139.
6. [En] R.Engelking, General Topology, PWN, Warszawa, 1977. MR 58:18316b
7. 1-topologies, Proceedings of the Amer. Math. Soc., 1966, vol. 17, 884-885. MR 33:1255
8. 1-complements, Pundamenta Mathematicae, 1967, vol. 61, 23-28. MR 37:5840
9. 1-complement for the reals, Proceedings of the Amer. Math. Soc., 1968, vol. 19, 177-179. MR 37:6897
10. [Wa1] S. Watson, Problems I wish I could solve, Open Problems in Topology, ed. by J. van Mill and G.M. Reed, Elsevier Science Publishers B.V. (North Holland), 1990, 37-76. CMP 91:03
11. [Wa2] S. Watson, The number of complements in the lattice of topologies on a fixed set, Topology and Its Applications, 1994, vol. 55, 101-125. MR 94k:54002