A generic theorem in the theory of cardinal invariants of topological spaces
Arhangel'skii, Aleksander V.
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 303-325 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.

Publié le : 1995-01-01
Classification:  54A25,  54D20 
@article{118759,
     author = {Aleksander V. Arhangel'skii},
     title = {A generic theorem in the theory of cardinal invariants of topological spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {303-325},
     zbl = {0837.54005},
     mrnumber = {1357532},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118759}
}

Arhangel'skii, Aleksander V. A generic theorem in the theory of cardinal invariants of topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 303-325. http://gdmltest.u-ga.fr/item/118759/

Arhangel'Skii A.V. On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955. (1969) | MR 0119188

Arhangel'Skii A.V. Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 33-96. (1978) | MR 0526012

Arhangel'Skii A.V. Theorems on the cardinality of families of sets in compact Hausdorff spaces, Soviet Math. Dokl. 17:1 (1976), 213-217. (1976) | MR 0405327

Arhangel'Skii A.V. A theorem on cardinality, Russ. Math. Surveys 34:4 (1979), 153-154. (1979) | MR 0548421

Arhangel'Skii A.V.; Hamdi M.M. Genedi The beginnings of the Theory of Relative Topological Properties, p. 3-48 in: General Topology. Spaces and Functions, Izd. MGU, Moscow, 1989 (in Russian).

Arhangel'Skii A.V. $C_p$-Theory, in: M. Hušek and J. van Mill, Editors, Chapter 1, p. 1-56, North-Holland, Amsterdam, 1992. | Zbl 0932.54015

Arhangel'Skii V.A. Relative compactness and networks, Master Thesis, Moscow State University, (1994), Preprint, p. 1-4, (in Russian).

Bell M.; Ginsburg J.; Woods G. Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79 (1978), 37-45. (1978) | MR 0526665

Burke D.K.; Hodel R.E. The number of compact subsets of a topological space, Proc. Amer. Math. Soc. 58 (1976), 363-368. (1976) | MR 0418014 | Zbl 0335.54005

Charlesworth A. On the cardinality of a topological space, Proc. Amer. Math. Soc. 66 (1977), 138-142. (1977) | MR 0451184 | Zbl 0364.54004

Corson H.H.; Michael E. Metrization of certain countable unions, Illinois J. Math. 8 (1964), 351-360. (1964) | MR 0170324

Dow A.; Vermeer J. An example concerning the property of a space being Lindelöf in another, Topology and Appl. 51 (1993), 255-260. (1993) | MR 1237391 | Zbl 0827.54014

Engelking R. General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. | MR 1039321 | Zbl 0684.54001

Fedorchuk V.V. On the cardinality of hereditarily separable compact Hausdorff spaces, Soviet Math. Dokl. 16 (1975), 651-655. (1975) | Zbl 0331.54029

Ginsburg J.; Woods G. A cardinal inequality for topological spaces involving closed discrete sets, Proc. Amer. Math. Soc. 64 (1977), 357-360. (1977) | MR 0461407 | Zbl 0398.54002

Grothendieck A. Criteres de compacticite dans les espaces fonctionnels genereaux, Amer. J. Math. 74 (1952), 168-186. (1952) | MR 0047313

Gryzlow A.A. Two theorems on the cardinality of topological spaces, Soviet Math. Dokl. 21 (1980), 506-509. (1980)

Hajnal A.; Juhász I. Discrete subspaces of topological spaces, Indag. Math. 29 (1967), 343-356. (1967) | MR 0229195

Hodel R.E. A technique for proving inequalities in cardinal functions, Topology Proc. 4 (1979), 115-120. (1979) | MR 0583694

Hodel R.E. Cardinal Functions, 1, in: Handbook of Set-theoretic Topology, Editors: Kunen K. and J.E. Vaughan, Chapter 1, 1-62, North-Holland, Amsterdam, 1984. | MR 0776620

Hodel R.E. Combinatorial set theory and cardinal function inequalities, Proc. Amer. Math. Soc. 111:2 (1991), 567-575. (1991) | MR 1039531 | Zbl 0713.54007

Mischenko A. Spaces with point countable bases, Soviet Math. Dokl. 3 (1962), 855-858. (1962)

Pol R. Short proofs of two theorems on cardinality of topological spaces, Bull. Acad. Polon. Sci. 22 (1974), 1245-1249. (1974) | MR 0383333 | Zbl 0295.54004

Ranchin D.V. On compactness modulo an ideal, Dokl. AN SSSR 202 (1972), 761-764 (in Russian). (1972) | MR 0296899

Shapirovskij B.E. On discrete subspaces of topological spaces; weight, tightness and Souslin number, Soviet Math. Dokl. 13 (1972), 215-219. (1972)

Shapirovskij B.E. Canonical sets and character. Density and weight in compact spaces, Soviet Math. Dokl. 15 (1974), 1282-1287. (1974) | Zbl 0306.54012

Stephenson R.M., Jr. Initially $\kappa $-compact and related spaces, in: Handbook of Set-theoretic Topology, Editors: Kunen K. and J.E. Vaughan, Chapter 13, 603-632, North-Holland, Amsterdam, 1984. | MR 0776632 | Zbl 0588.54025

Van Douwen Eric K. Applications of maximal topologies, Topol. and Appl. 51:2 (1993), 125-139. (1993) | MR 1229708 | Zbl 0845.54028