@article{RM_1997_52_5_a3,
author = {A. V. Arkhangel'skii},
title = {Some recent advances and open problems in general topology},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {929--953},
year = {1997},
volume = {52},
number = {5},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_1997_52_5_a3/}
}
A. V. Arkhangel'skii. Some recent advances and open problems in general topology. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 52 (1997) no. 5, pp. 929-953. http://geodesic.mathdoc.fr/item/RM_1997_52_5_a3/
[1] Alexandroff P. S., “Über die Metrisation der in kleinen kompakten topologischen Raüme”, Math. Ann., 92 (1924), 294–301 | DOI | MR
[2] Alexandroff P. S., Urysohn P. S., “Mémoire sur les espaces topologiques compacts”, Verh. Akad. Wetensch. Amsterdam, 14, 1929
[3] Arkhangelskii A. V., “Svoistvo parakompaktnosti v klasse sovershenno normalnykh, lokalno bikompaktnykh prostranstv”, Dokl. AN SSSR, 203 (1972), 1231–1234 | MR
[4] Arkhangelskii A. V., “Topologicheskaya odnorodnost. Topologicheskie gruppy i ikh nepreryvnye obrazy”, UMN, 42:2 (1987), 69–105 | MR
[5] Arhangelskiĭ A. V., “Some problems and lines of investigation in General Topology”, Comment. Math. Univ. Carolin., 29:4 (1988), 611–629 | MR
[6] Arhangelskiĭ A. V., “Problems in $C_p$-theory”, Open Problems in Topology, Ch. 31, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 603–615
[7] Arkhangelskii A. V., “Prostranstva otobrazhenii i koltsa nepreryvnykh funktsii”, Itogi nauki i tekhniki. Sovr. probl. matem. Fundam. napr., 51, VINITI, M., 1989, 81–171 | MR
[8] Arkhangelskii A. V., Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989
[9] Arhangel'skiĭ A. V., “The general concept of cleavability of a topological space”, Topology Appl., 44:1–3 (1992), 27–36 | DOI | MR | Zbl
[10] Arhangel'skiĭ A. V., “Cleavability over reals”, Topology Appl., 48:2 (1992), 163–178 | DOI | MR | Zbl
[11] Arhangel'skiĭ A. V., “$C_p$-theory”, Recent progress in General Topology, Ch. 31, eds. M. Hus̆ek, J. van Mill, North-Holland, Amsterdam, 1992, 1–56
[12] Arhangel'skiĭ A. V., “On cleavability of topological spaces over $R$, $R^n$ and $R^{\omega}$”, Ann. New York Acad. Sci., 659 (1992), 18–28 | DOI
[13] Arhangel'skiĭ A. V., “A survey of cleavability”, Topology Appl., 54:1–3 (1993), 141–163 | DOI | MR | Zbl
[14] Arhangel'skiĭ A. V., “On countably compact topologies on compact groups and on dyadic compacta”, Topology Appl., 57:2–3 (1994), 163–181 | DOI | MR | Zbl
[15] Arhangel'skiĭ A. V., “A generic theorem in the theory of cardinal invariants of topological spaces”, Comment. Math. Univ. Carolin., 36:2 (1995), 303–325 | MR | Zbl
[16] Arhangel'skiĭ A. V., “On a Theorem of Grothendieck in $C_p$-theory”, Topology Appl., 1997, 1–21 | DOI | Zbl
[17] Arhangel'skiĭ A. V., “Embeddings in $C_p$-spaces”, Topology Appl., 1997 (to appear)
[18] Arhangel'skiĭ A. V., Cioban M. M., “On continuous mappings of $C_p$-spaces and extenders”, Trudy MIRAN, 212, 1996, 33–36
[19] Arkhangelskii A. V., Fedorchuk V. V., “Ob uplotneniyakh schetno kompaktnykh prostranstv na kompakty”, Fundament. nauka i prikl. matem., 4 (1995), 871–880 | MR
[20] Arkhangelskii A. V., Ponomarev V. I., Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974
[21] Arkhangelskii A. V., Shakhmatov D. B., “O tochechnoi approksimatsii proizvolnykh funktsii schetnymi semeistvami nepreryvnykh funktsii”, Trudy sem. Petrovskogo, 13, 1988, 206–227; 259
[22] Baars J., de Groot J., “An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces”, Comment. Math. Univ. Carolin., 29 (1988), 577–595 | MR | Zbl
[23] Baars J., de Groot J., van Mill J., Pelant J., “An example of $l_p$-equivalent spaces which are not $l^\ast_p$-equivalent”, Proc. Amer. Math. Soc., 119:3 (1993), 963–969 | DOI | MR | Zbl
[24] Baars J., de Groot J., Pelant J., “Function spaces on completely metrizable spaces”, Trans. Amer. Math. Soc., 340 (1993), 871–879 | DOI | MR
[25] Balogh Z., “A normal screenable nonparacompact space in $ZFC$” (to appear)
[26] Balogh Z., “On collectionwise normality of locally compact spaces”, Trans. Amer. Math. Soc., 323 (1991), 389–411 | DOI | MR | Zbl
[27] Balogh Z., “A paracompact $Q$-space without a $G_\delta$-diagonal” (to appear)
[28] Banach S., “Livre Ecossais, Problem 1”, 17.VII.1935, Colloq. Math., 1:2 (1948), 150
[29] Bing R. H., “Metrization of topological spaces”, Canad. J. Math., 3 (1951), 175–186 | MR | Zbl
[30] Bouziad A., Calbrix J., “Čech-complete spaces and upper topology”, Topology Appl., 70 (1996), 133–138 | DOI | MR | Zbl
[31] Burke D., “A nondevelopable locally compact Hausdorff space with a $G_\delta$-diagonal”, Topology Appl., 2 (1972), 287–291 | DOI | MR | Zbl
[32] Buzyakova R. Z., “O rasscheplyaemykh prostranstvakh”, Vestnik MGU. Ser. 1 matem., mekh., 1993, no. 6, 83–84 | MR | Zbl
[33] Buzyakova R. Z., “O proizvedenii normalnykh prostranstv”, Vestnik MGU. Ser. 1 matem., mekh., 1994, no. 4, 81–82 | MR | Zbl
[34] Buzyakova R. Z., “Ob obrazakh dekartovykh proizvedenii pri uplotneniyakh”, Vestnik MGU. Ser. 1 matem., mekh., 1996, no. 1, 17–19 | MR
[35] Buzyakova R. Z., “O rasscheplyaemosti kompaktov nad lineino uporyadochennymi prostranstvami”, Vestnik MGU. Ser. 1 matem., mekh., 1996, no. 3 | MR
[36] Buzyakova R. Z., “Primer dvukh normalnykh topologicheskikh grupp, proizvedenie kotorykh ne uplotnyaetsya na normalnoe prostranstvo”, Vestnik MGU. Ser. 1 matem., mekh. (to appear)
[37] Buzyakova R. Z., “A criterion that a pseudocompact space condenses onto a compact space”, Questions Answers Gen. Topology, 1996 (to appear)
[38] Davis S., “A non-developable Čech-complete space with a point-countable base”, Proc. Amer. Math. Soc., 78 (1980), 139–142 | DOI | MR | Zbl
[39] Debs G., Saint Raymond J., “Compact covering and game determinacy”, Topology Appl., 68 (1996), 153–185 | DOI | MR | Zbl
[40] Debs G., Saint Raymond J., “Compact covering properties of finite-to-one mappings” (to appear) | Zbl
[41] Delistathis G., Watson S., A regular space with a countable network and different dimensions, Preprint
[42] van Douwen E. K., “Nonhomogeneity of products of preimages and $\pi$-weight”, Proc. Amer. Math. Soc., 69 (1978), 183–192 | DOI | MR | Zbl
[43] van Douwen E. K., “A technique for constructing honest locally compact submetrizable examples”, Topology Appl., 47 (1992), 179–201 | DOI | MR | Zbl
[44] Eckertson F., Fleissner W., Korovin A., Levy R., “Not realcompact images of not Lindelöf spaces”, Topology Appl., 58 (1994), 115–125 | DOI | MR | Zbl
[45] Engelking R., General Topology, PWN, Warsaw, 1977 | Zbl
[46] Gruenhage G., Koszmider P., “The Arhangel'skiĭ–Tall problem: a consistent counterexample”, Fund. Math., 149 (1996), 143–166 | MR | Zbl
[47] Gruenhage G., Koszmider P., “The Arhangel'skiĭ–Tall problem under Martin's axiom”, Fund. Math. (to appear)
[48] Gul'ko S. P., “Uniformly homeomorphic spaces of functions”, Proc. Steklov Inst. Math., 3, 1993, 87–93 | MR
[49] Heath R. W., “On spaces with point-countable bases”, Bull. Acad. Polon. Sci. Math. Ser., 13 (1965), 393–395 | MR | Zbl
[50] Ivanov A. V., “O bikompaktakh, vse konechnye stepeni kotorykh nasledstvenno separabelny”, Dokl. AN SSSR, 243:5 (1978), 1109–1112 | MR | Zbl
[51] Just W., Wicke H., “Some conditions under which tri-quotient or compact-covering maps are inductively perfect”, Topology Appl., 55 (1994), 289–305 | DOI | MR | Zbl
[52] Katetov M., “On mappings of countable spaces”, Colloq. Math., 2 (1949), 30–33 | MR | Zbl
[53] Kawamura K., Morishita K., “Linear topological classification of certain function spaces on manifolds and $CW$-complexes”, Topology Appl., 69:3 (1996), 265–282 | DOI | MR | Zbl
[54] Kombarov A. P., “O slaboi normalnosti prostranstva $X^2\setminus\Delta$”, Vestnik MGU. Ser. 1 matem., mekh., 1995, no. 3, 40–44 | MR | Zbl
[55] Kulpa W., “A minimization of $0$-dimensional metric spaces”, Colloq. Math., 36:2 (1976), 215–216 | MR | Zbl
[56] Leiderman A., Morris S. A., Pestov V., The free Abelian topological group and the free locally convex space on the unit interval, Preprint
[57] Marciszewski W., “A countable $X$ having a closed subspace $A$ with $C_p(A)$ not a factor of $C_p(X)$”, Topology Appl., 64 (1995), 141–147 | DOI | MR | Zbl
[58] Marciszewski W., A function space $C_p(X)$ not linearly homeomorphic to $C_p(X)\times R$, Preprint, 1996
[59] Marron D. J., Splittability in ordered sets and in ordered spaces, Ph. D. Dissertation, Faculty of Science, Queens University of Belfast, 1996
[60] van Mill J., Pol R., “A countable space with a closed subspace without measurable extender”, Bull. Acad. Polon. Sci., 41 (1993), 279–283 | MR | Zbl
[61] Michael E., “Some problems”, Open Problems in Topology, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 271–278 | MR
[62] Mischenko A. S., “O finalno kompaktnykh prostranstvakh”, Dokl. AN SSSR, 145 (1962), 1224–1227 | MR | Zbl
[63] Nadler S. B., Quinn J., Reiter H., “Results and problems concerning compactifications, compact subtopologies, and mappings”, Fund. Math., 89:1 (1975), 33–44 | MR | Zbl
[64] Nagami K., “Paracompactness and strong screenability”, Nagoya Math. J., 8 (1955), 83–88 | MR | Zbl
[65] Nikiel J., “On continuous images of arcs and compact ordered spaces”, Topology Proc., 14 (1989), 163–193, 279–280 | MR | Zbl
[66] Nyikos P., “On first countable, countably compact spaces. 3: The problem of obtaining separable noncompact examples”, Open Problems in Topology, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 127–162 | MR
[67] Okromeshko N. G., “O retraktsiyakh odnorodnykh prostranstv”, Dokl. AN SSSR, 268:3 (1983), 548–551 | MR | Zbl
[68] Okunev O. G., “On Lindelöf sets of continuous functions”, Topology Appl., 63 (1995), 91–96 | DOI | MR | Zbl
[69] Okunev O. G., “Homeomorphisms of function spaces and hereditary cardinal invariants”, Topology Appl., 1997 (to appear) | MR
[70] Ostrovskii A. V., “Novyi klass otobrazhenii, svyazannyi s kompaktno nakryvayuschimi otobrazheniyami”, Vestnik MGU. Ser. 1 matem., mekh., 1994, no. 4, 24–27 | MR
[71] Pavlov O., Uplotneniya stepenei nepsevdokompaktnykh prostranstv na $\sigma$-kompaktnye prostranstva, Doklad na topologicheskom seminare A. V. Arkhangelskogo (1995, Moskva)
[72] Pestov V. G., “Sovpadenie razmernostei $\dim$ $l$-ekvivalentnykh topologicheskikh prostranstv”, Dokl. AN SSSR, 266:3 (1982), 553–556 | MR | Zbl
[73] Pol R., “On metrizable $E$ with $C_p(E)$ not linearly homeomorphic to $C_p(E)\times C_p(E)$”, Matematika, 42 (1995), 49–55 | MR | Zbl
[74] Pytkeev E. G., “O supremume topologii”, Matem. zametki, 20:4 (1976), 489–500 | MR | Zbl
[75] Pytkeev E. G., “K teorii uplotnenii na kompakty”, Dokl. AN SSSR, 233:6 (1977), 1046–1048 | MR | Zbl
[76] Pytkeev E. G., “O sekventsialnosti prostranstv nepreryvnykh funktsii”, UMN, 37:5 (1982), 197–198 | MR | Zbl
[77] Rudin M. E., “A normal, screenable, non-paracompact space”, Topology Appl., 15 (1983), 313–322 | DOI | MR | Zbl
[78] Rudin M. E., “Some conjectures”, Open Problems in Topology, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 185–193
[79] Rudin M. E., The Abstract and the Talk at the Topology Conference in Prague, 1996
[80] Sakai M., “On embeddings into $C_p(X)$ where $X$ is Lindelöf”, Comment. Math. Univ. Carolin., 33 (1992), 165–171 | MR | Zbl
[81] Shakhmatov D. B., “O psevdokompaktnykh prostranstvakh s tochechno schetnoi bazoi”, Dokl. AN SSSR, 279:4 (1984), 825–829 | MR | Zbl
[82] Shakhmatov D. B., “A pseudocompact Tychonoff space all countable subsets of which are closed and $C^\ast$-embedded”, Topology Appl., 22 (1986), 139–144 | DOI | MR | Zbl
[83] Sipacheva O. V., “O lindelefovykh podprostranstvakh prostranstv funktsii nad lineino uporyadochennymi separabelnymi kompaktami”, Obschaya topologiya, prostranstva i funktsii, Izd-vo MGU, M., 1989, 143–148 | MR
[84] Tall F., “Tall's Problems”, Open Problems in Topology, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 21–35 | MR
[85] Tkachuk V. V., “O bikompaktifikatsiyakh”, Vestnik MGU. Ser. 1 matem., mekh., 1990
[86] Tkachuk V. V., “A note on splittable spaces”, Comment. Math. Univ. Carolin., 33:3 (1992), 551–555 | MR | Zbl
[87] Velichko N. V., “Lindelöf property is preserved by $l$-equivalence”, The Talk at 7th Prague Topology Symposium, 1991; Preprint
[88] Watson S., “Problems I wish I could solve”, Open Problems in Topology, eds. J. van Mill, G. M. Reed, North-Holland, Amsterdam, 1990, 37–76
[89] Watson S., “Locally compact normal spaces in the constructible universe”, Canad. J. Math., 34 (1982), 1091–1096 | MR | Zbl
[90] Yakivchik A. N., “Slabo normalnye topologicheskie prostranstva i proizvedeniya”, Vestnik MGU. Ser. 1 matem., mekh., 1994, no. 6, 82
[91] Yakivchik A. N., “Dopolnenie k teoreme Tamano”, Vestnik MGU. Ser. 1 matem., mekh., 1994, no. 6, 83–84
[92] Yaschenko I. V., “Vlozheniya v $R^n$ i $R^\omega$ i rasscheplyaemost”, Vestnik MGU. Ser. 1 matem., mekh., 1992, no. 2, 107
[93] Yaschenko I. V., “Cardinality of discrete families of open sets and one-to-one continuous mappings”, Questions Answers Gen. Topology, 2 (1992), 24–26