The Tamano Theorem in $\Cal MAP$
Buhagiar, David
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 755-770 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper we continue with the study of paracompact maps introduced in [1]. We give two external characterizations for paracompact maps including a characterization analogous to The Tamano Theorem in the category $\Cal TOP$ (of topological spaces and continuous maps as morphisms). A necessary and sufficient condition for the Tychonoff product of a closed map and a compact map to be closed is also given.

Publié le : 1999-01-01
Classification:  54B30,  54C05,  54C10,  54C99 
@article{119128,
     author = {David Buhagiar},
     title = {The Tamano Theorem in $\Cal MAP$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {755-770},
     zbl = {1010.54014},
     mrnumber = {1756550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119128}
}

Buhagiar, David. The Tamano Theorem in $\Cal MAP$. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 755-770. http://gdmltest.u-ga.fr/item/119128/

Buhagiar D. Paracompact maps, Questions Answers Gen. Topology 15 (1997), 2 203-223. (1997) | MR 1472184 | Zbl 0997.54012

Buhagiar D. The category ${\mathscr{MAP}}$, submitted for publication, 1998.

Buhagiar D.; Miwa T. Covering properties on maps, Questions Answers Gen. Topology 16 (1998), 1 53-66. (1998) | MR 1614753 | Zbl 0997.54033

Buhagiar D.; Miwa T.; Pasynkov B.A. On metrizable type $({MT}$-$)$ maps and spaces, to appear in Topology Appl. | MR 1701238 | Zbl 0953.54017

Dieudonné J. Une généralisation des espaces compacts, J. de Math. Pures et Appl. 23 (1944), 65-76. (1944) | MR 0013297

Engelking R. General Topology, revised ed., Heldermann, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

James I.M. Spaces, Bull. London Math. Soc. 18 (1986), 529-559. (1986) | MR 0859946 | Zbl 0647.05005

James I.M. Fibrewise Topology, Cambridge Univ. Press, Cambridge, 1989. | MR 1010230 | Zbl 1147.55001

Johnstone P.T. The Gleason cover of a topos II, J. Pure Appl. Algebra 22 (1981), 229-247. (1981) | MR 0629332 | Zbl 0445.18005

Johnstone P.T. Wallman compactification of locales, Houston J. Math. 10 (1984), 201-206. (1984) | MR 0744904 | Zbl 0549.54018

Künzi H.P.A.; Pasynkov B.A. Tychonoff compactifications and R-completions of mappings and rings of continuous functions, Categorical Topology (L'Aquila, 1994), Kluwer Acad. Publ., Dordrecht, 1996, pp.175-201. | MR 1412584

Lever D. Continuous families: Categorical aspects, Cahiers de topologie et géométrie différentielle 24 (1983), 393-432. (1983) | MR 0749470 | Zbl 0535.18004

Lever D. Relative topology, Categorical Topology, Proc. Conference Toledo, Ohio, 1983, Heldermann, Berlin, 1984. | MR 0785023 | Zbl 0555.18006

Morita K. Paracompactness and product spaces, Fund. Math. 50 (1962), 223-236. (1962) | MR 0132525 | Zbl 0099.17401

Pasynkov B.A. On extension to mappings of certain notions and assertions concerning spaces (in Russian), Mappings and Functors, Izdat. MGU, Moscow, 1984, pp.72-102. | MR 0791256

Pasynkov B.A. Elements of the general topology of continuous maps (in Russian), On Compactness and Completeness Properties of Topological Spaces, ``FAN'' Acad. of Science of the Uzbek. Rep., Tashkent, 1994, pp.50-120.

Preuss G. Theory of topological structures (an approach to categorical topology), Mathematics and its Applications, D.Reidel Publishing Company, Dordrecht, Holland, 1987. | MR 0937052 | Zbl 0649.54001

Tamano H. On paracompactness, Pacific J. Math. 10 (1960), 1043-1047. (1960) | MR 0124876 | Zbl 0094.35403

Tamano H. On compactifications, J. Math. Kyoto Univ. 1 (1962), 161-193. (1962) | MR 0142096 | Zbl 0106.15601

Ulyanov V.M. On compact extensions of countable character and absolutes (in Russian), Math. Sb. 98 (1975), 2 223-254. (1975) | MR 0394534

Vainstein I.A. On closed maps of metric spaces (in Russian), Doklady Akad. Nauk SSSR 57 (1947), 319-321. (1947) | MR 0022067

Whyburn G.T. A unified space for mappings, Trans. Amer. Math. Soc. 74 (1953), 2 344-350. (1953) | MR 0052762 | Zbl 0053.12303

Whyburn G.T. Compactification of mappings, Math. Ann. 166 (1966), 1 168-174. (1966) | MR 0200905 | Zbl 0141.20505