On half-completion and bicompletion of quasi-metric spaces
Alemany, Elena ; Romaguera, Salvador
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 749-756 / Harvested from Czech Digital Mathematics Library
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We characterize the quasi-metric spaces which have a quasi-metric half-comp\-le\-tion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space $X$ is quasi-metric if and only if $X$ is finite.

Publié le : 1996-01-01
Classification:  54E15,  54E35,  54E50 
@article{118882,
     author = {Elena Alemany and Salvador Romaguera},
     title = {On half-completion and bicompletion of quasi-metric spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {749-756},
     zbl = {0886.54027},
     mrnumber = {1440705},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118882}
}

Alemany, Elena; Romaguera, Salvador. On half-completion and bicompletion of quasi-metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 749-756. http://gdmltest.u-ga.fr/item/118882/

Császár A. Extensions of quasi-uniformities, Acta Math. Hungar. 37 (1981), 121-145. (1981) | MR 0616884

Deák J. On the coincidence of some notions of quasi-uniform completeness defined by filters pairs, Studia Sci. Math. Hungar. 26 (1991), 411-413. (1991) | MR 1197089

Deák J. A bitopological view of quasi-uniform completeness I, II, III, Studia Sci. Math. Hungar., Part I, 30 (1995), 389-409; Part II, 30 (1995), 411-431; Part III, to appear. | MR 1353614

Deák J. Extending and completing quiet quasi-uniformities, Studia Sci. Math. Hungar. 29 (1994), 349-362. (1994) | MR 1304888

Deák J.; Romaguera S. Co-stable quasi-uniform spaces, Ann. Univ. Sci. Budapest 38 (1995), 55-70. (1995) | MR 1376415

Doitchinov D. On completeness of quasi-uniform spaces, C.R. Acad. Bulg. Sci. 41 (1988), 5-8. (1988) | MR 0959596 | Zbl 0649.54015

Fletcher P.; Hunsaker W. Uniformly regular quasi-uniformities, Top. Appl. 37 (1990), 285-291. (1990) | MR 1082939 | Zbl 0707.54021

Fletcher P.; Hunsaker W. Completeness using pairs of filters, Top. Appl. 44 (1992), 149-155. (1992) | MR 1173251 | Zbl 0770.54027

Fletcher P.; Lindgren W.F. Quasi-Uniform Spaces, Dekker, 1982. | MR 0660063 | Zbl 0583.54017

Künzi H.P.A.; Mrsevic M.; Reilly I.L.; Vamanamurthy M.K. Convergence, precompactness and symmetry in quasi-uniform spaces, Math. Japonica 38 (1993), 239-253. (1993) | MR 1213385

Künzi H.P.; Romaguera S.; Salbany S. Topological spaces that admit bicomplete quasi-pseudometrics, Ann. Univ. Sci. Budapest 37 (1994), 185-195. (1994) | MR 1303429

Künzi H.P.A. On strongly quasi-metrizable spaces, Archiv Math. (Basel) 41 (1983), 57-63. (1983) | MR 0713668

Künzi H.P.A. Complete quasi-pseudo-metric spaces, Acta Math. Hungar. 59 (1992), 121-146. (1992) | MR 1160209

Reilly I.L.; Subrahmanyam P.V.; Vamanamurthy M.K. Cauchy sequences in quasi- pseudo-metric spaces, Monatsh. Math. 93 (1982), 127-140. (1982) | MR 0653103 | Zbl 0472.54018

Romaguera S. Left $K$-completeness in quasi-metric spaces, Math. Nachr. 157 (1992), 15-23. (1992) | MR 1233044 | Zbl 0784.54027

Romaguera S. Left $K$-complete quasi-uniform spaces, Seminar. Fach. Math. Fern Univ. Hagen 48 (1994), 101-114. (1994) | MR 1467766

Romaguera S. On hereditary precompactness and completeness in quasi-uniform spaces, Acta Math. Hungar., to appear. | MR 1415928 | Zbl 0924.54035

Romaguera S.; Gutiérrez A. A note on Cauchy sequences in quasi-pseudometric spaces, Glasnik Mat. 21 (1986), 191-200. (1986) | MR 0866764

Romaguera S.; Salbany S. On bicomplete quasi-pseudometrizability, Top. Appl. 50 (1993), 283-289. (1993) | MR 1227555 | Zbl 0827.54020

Salbany S. Bitopological Spaces, Compactifications and Completions, Math. Monographs, Univ. Cape Town, no. 1, 1974. | MR 0425919 | Zbl 0353.54021

Salbany S.; Romaguera S. On countably compact quasi-pseudometrizable spaces, J. Austral. Math. Soc. (Series A) 49 (1990), 231-240. (1990) | MR 1061043 | Zbl 0706.54027

Stoltenberg R.A. On quasi-metric spaces, Duke Math. J. 36 (1969), 65-72. (1969) | MR 0235515 | Zbl 0176.51902