Partial discretization of topologies
Bonanzinga, M. ; Cammaroto, F. ; Matveev, M. V.
Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000), p. 485-503 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.

Publié le : 2000-06-01
@article{BUMI_2000_8_3B_2_485_0,
     author = {M. Bonanzinga and F. Cammaroto and M. V. Matveev},
     title = {Partial discretization of topologies},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3-A},
     year = {2000},
     pages = {485-503},
     zbl = {0993.54001},
     mrnumber = {1769998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_2_485_0}
}

Bonanzinga, M.; Cammaroto, F.; Matveev, M. V. Partial discretization of topologies. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 485-503. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_2_485_0/

[1] Balasubramanian, G., On some generalization of compact space, Glasnik Mat., 17 (37) (1982), 367-380. | MR 692509 | Zbl 0514.54015

[2] Berner, A. J., Spaces without dense conditionally compact subsspaces, Proc. Amer. Math. Soc., 81 (1979), 187-192. | MR 589156 | Zbl 0471.54008

[3] Bonanzinga, M., Preservation and reflection of acc and hacc spaces, Comment. Math. Univ. Carol., 37, No. 1 (1996), 147-153. | MR 1396166 | Zbl 0917.54027

[4] Bonanzinga, M., On the product of a compact space with a hereditarily absolutely countably compact space, Comment. Math. Univ. Carol., 38,3 (1997), 557-562. | MR 1485076 | Zbl 0937.54013

[5] Bonanzinga, M., Star-Lindelöf and absolutely star-Lindelöf spaces, Questions and Answers in Gen. Topol., 16, No. 2 (1998). | MR 1642032 | Zbl 0931.54019

[6] Bonanzinga, M.-Matveev, M. V., Centered-Lindelöfness versus star-Lindelöfness, to appear in Comment. Math. Univ. Carol. | MR 1756931 | Zbl 1037.54502

[7] Cammaroto, F.-Santoro, G., Some counterexamples and properties on generalizations of Lindelöf spaces, Internat. J. Math. and Math. Sci., 19 (1996), No. 4, 737-746. | MR 1397840 | Zbl 0860.54033

[8] Van Douwen, E. K.-Reed, G. M.-Roscoe, A. W.-Tree, I. J., Star covering properties, Topol. and Appl., 39 (1991), 71-103. | MR 1103993 | Zbl 0743.54007

[9] Frolik, Z., Generalizations of compact and Lindelöf spaces, Czechoslovak Math. J., 9 (84) (1959), 172-217 (in Russian). | MR 105075 | Zbl 0098.14201

[10] Engelking, R., General Topology, Warszawa (1977). | MR 500780 | Zbl 0373.54002

[11] Ginsburg, J.-Saks, A., Some applications of ultrafilters in topology, Pacific J. Math., 57 (1975), 403-418. | MR 380736 | Zbl 0288.54020

[12] Malykhin, V. I., Everywhere dense subspaces of topological spaces, General Topology, Moscow State Univ. Publ., Moscow (1986), 65-76. | MR 1080759

[13] Matveev, M. V., On everywhere dense zero dimensional subspaces of topological spaces, Vestnik MGU, (1981), No. 4, 36-39. | MR 631506 | Zbl 0466.54019

[14] Matveev, M. V., Inverse compactness, Topol. and Appl., 62 (1995), 181-191. | MR 1320251 | Zbl 0837.54013

[15] Matveev, M. V., Absolutely countably compact spaces, Topol. and Appl., 58 (1994), 81-92. | MR 1280711 | Zbl 0801.54021

[16] Matveev, M. V., A countably compact topological group which is not absolutely countably compact, Questions and Answers in Gen. Topol., 11 (1993), 173-176. | MR 1234212 | Zbl 0808.54025

[17] Matveev, M. V., Closed embeddings into pseudocompact spaces, Mat. Zametki, 41 (1984), 377-394 (in Russian; English translation in: Math. Notes). | Zbl 0629.54008

[18] Matveev, M. V., Some questions on property (a), Questions and Answers in Gen. Topol., 15 (1997), 103-111. | MR 1472172 | Zbl 1002.54016

[19] Van Mill, J.-Vaughan, J. E., Is ω*-u absolutely countably compact?, Ann. New York Akad. Sci., 767 (1995), 161-164. | MR 1462391 | Zbl 0918.54021

[20] Porter, J. R.-Woods, R. G., Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag (1988). | MR 918341 | Zbl 0652.54016

[21] Reznichenko, E. A., A pseudocompact space in which only sets of full cardinality are not closed and not discrete, Vestnik MGU Ser. 1 (1989), No. 6, 69-71 (in Russian; English translation in: Moscow Univ. Math. Bull). | Zbl 0725.54018

[22] Roitman, J., Basic S- and L-spaces, Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan Eds., Elsevier Sci. Pub. (1984), 295-326. | MR 776626 | Zbl 0594.54001

[23] Rudin, M. E.-Stares, I. S.-Vaughan, J. E., From countable compactness to absolute countable compactness, to appear in Proc. A.M.S. | MR 1415367 | Zbl 0984.54027

[24] Shakhmatov, D. B., A pseudocompact Tychonoff space all countable subsets of which are closed and C*-embedded, Topol. and Appl., 22 (1986), 139-144. | MR 836321 | Zbl 0586.54020

[25] Stephenson, R. M. Jr., Moore-closed and first-countable feebly compact extension spaces, Topol. and Appl., 27 (1987), 11-28. | MR 910491 | Zbl 0633.54012

[26] Syngal, M. K.-Araya, S. P., On almost regular spaces, Glasnik Mat., 4(24) (1969), 89-99. | Zbl 0169.24902

[27] Vaughan, J. E., A countably compact separable space which is not absolutely countably compact, Comment. Mat. Univ. Carol., 36:1 (1995), 197-201. | MR 1334426 | Zbl 0833.54012

[28] Willard, S.-Dissanayake, U. N. B., The almost Lindelöf degree, Canad. Math. Bull., 27 (4) (1984), 36-41. | MR 763044 | Zbl 0551.54003