References
D. Adnadževič, Some properties of A-spaces. Soviet Math. Doklady14, 492–496 (1973); translated from Doklady Akad. Nauk SSSR209, 761–764 (1973) (Russian).
P. Alexandrov, Diskrete Räume. Mat. Sb.2, 501–519 (1937).
A. V. Arhangel'skii andR. Wiegandt, Connectednesses and disconnectednesses in topology. General Topology Appl.5, 9–33 (1975).
C. E. Aull, Separation of bicompact sets. Math. Ann.158, 197–202 (1965).
C. E. Aull, Sequences in topological spaces. Prace Matematiczne2, 329–336 (1968).
C. E. Aull, Properties of side points of sequences. General Topology Appl.1, 201–208 (1971).
C. E. Aull, A separation axiom of F. Riesz. Acta Math. Acad. Sci. Hungar.24, 77–84 (1973).
R. W. Bagley, Topological space with unique limits. Problem 4694. Amer. Math. Monthly64, 376 (1957).
V. K. Balachandran, Minimal bicompact spaces. J. Ind. Math. Soc., N.S.12, 47–48 (1948) [Math. Reviews10, (1949), p. 390].
S. Baron, Reflectors as compositions of epi-reflectors. Trans. Amer. Math. Soc.136, 499–508 (1969).
N.Bourbaki, General Topology. Part 1 (Engl. transi.). Paris 1966.
D. E. Cameron, Maximal and minimal topologies. Trans. Amer. Math. Soc.160, 229–248 (1971).
H. F. Cullen, Unique sequential limits. Boll. Un. Mat. Ital.20, 123–124 (1965).
W. F. Davison, Mosaics of compact metric spaces. Trans. Amer. Math. Soc.91, 525–546 (1959).
B.Day, Limit spaces and closed span categories. In: Proc. Sydney Category Theory Seminar 1972/1973, ed. by G. M. Kelly. LNM420, 65–74 (1974).
W. Dunham, Weakly Hausdorff spaces. Kyungpook Math. J.15, 41–50 (1975) [Math. Reviews51, 9019 (1976)].
Editorial Note, Amer. Math. Monthly72, 645 (1965).
S. P. Franklin, Spaces in which sequences suffice. Fund. Math.57, 107–115 (1965). II. Fund. Math.61, 51–56 (1967).
S. P. Franklin andL. C. Robertson,O-sequences andO-nets. Amer. Math. Monthly72, 506–510 (1965).
A. Gabcía-máynez, OnKC andk-spaces. An. Inst. Mat., Univ. Nac. Autónoma México15, 33–50 (1976) [Zbl. Math.332, 54022 (1977)].
A. GabcÍa-Máynez, Some generalizations of the Hausdorff separation axiom. Bol. Soc Mat. Mexicana (2)16, 38–41 (1971) [Math. Reviews49, 1477 (1975)].
M. Gemignani, Problem 5269. Amer. Math. Monthly72, 194 (1965).
E. Halfar, A note on Hausdorff separation. Amer. Math. Monthly68, 164 (1961).
H.Herrlich, Topologische Reflexionen und Coreftexionen. Lect. Notes in Math.78, Berlin-Heidelberg-New York 1968.
E. Hewitt, A problem of set-theoretic topology. Duke Math. J.10, 309–333 (1943).
M. Hochster, Prime ideal structure in commutative rings. Trans. Amer. Math. Soc.142, 43–60 (1969).
R.-E.Hoffmann, Factorization of cones (I). Math. Nachrichten (to appear).
R.-E.Hoffmann, Factorization of cones (II). (in preparation).
R.-E. Hoffmann, Irreducible filters and sober spaces. Manuscripta Math.22, 365–380 (1977).
A. J. Insel, A note on the Hausdorff separation property in first countable spaces. Amer. Math. Monthly72, 289–290 (1965).
J. E. Joseph, Continuous functions and spaces in which compact sets are closed. Amer. Math. Monthly76, 1125–1126 (1969).
J. E. Joseph, Spaces in which compact sets are closed. Mathematics magazine49, 90 (1976).
J. E. Joseph, Characterizations of maximal topologies. J. Austral. Math. Soc., Ser. A,21, 334–336 (1976).
M. Kim, A compact graph theorem. Mathematics magazine47, 99 (1974).
W. F.La Martin, On the foundations ofk-group theory. Dissertationes Mathematicae146. Warszawa 1977.
W. F. La Martin, Epics in the category ofT 2 T-groups need not have dense range. Colloquium Math.36, 37–41 (1976).
L. D. Lavallee, The one-point countable compactification of curve spaces and arc spaces. Portugaliae Math.24, 105–114 (1965).
J. Lawson andB. Madison, Quotients ofk-semigroups. Semigroup Forum9, 1–18 (1974).
J.Lawson and B.Madison, Comparisons of notions of weak Hausdorffness. In: Topology, Proc. Memphis State Univ. Conf. 1975, ed. by S. P. Franklin and B. V. Smith Thomas, pp. 207–215. New York-Basel 1976.
N. Levine, When are compact and closed equivalent? Amer. Math. Monthly72, 41–44 (1965).
N. Levine, On the intersection of two compact sets. Rend. Circ. Mat. Palerma (2)17, 283–288 (1968).
N. Levine, A note on convergence in topological spaces. Amer. Math. Monthly67, 667–668 (1960).
M. C. Mccord, Classifying spaces and infinite symmetric products. Trans. Amer. Math. Soc.146, 273–298 (1969).
T. K. Mukherji, On weak Hausdorff spaces. Bull. Calcutta Math. Soc.58, 153–157 (1966).
M. G. Murdeshwar andS. A. Naimpally, Semi-Hausdorff spaces. Canad. Math. Bull.9, 353–356 (1966).
T. Noiri, Remarks on weak Hausdorff spaces. Bull. Calcutta Math. Soc.66, 33–37 (1974).
T. Noiri, Remarks on unique sequential limits. Boll. Un. Mat. Ital. (4)7, 192–196 (1973).
E. C. Nummela,K-groups generated byK-spaces. Trans. Amer. Math. Soc.201, 279–289 (1975).
G. Preuss, Eine Galois-Korrespondenz in der Topologie. Monatsh. Math.75, 447–452 (1971).
M. J. Reed, Hausdorff-like separation properties and generalizations of the first countability axiom. Tamkang J. Math.5, 197–201 (1974) [Math. Reviews53, 1519 (1977)].
W. Sierpinski, Sur les relations entre quelques propriétés fondamentales des espaces topologiques. Soc. Sci. Lett, de Varsovie. C. R. Classe III. Sci. Math. Phys.40 (1947), 66–78 (1948) [Math. Reviews12, 195 (1951)].
F. Siwieć, Generalizations of the first axiom of countability. Rocky Mountain J. Math.5, 1–60 (1975).
P. Slepian, A non-Hausdorff topology such that each convergent sequence has exactly one limit. Amer. Math. Monthly71, 776–778 (1964).
N. Smythe andC. A. Wilkins, Minimal Hausdorff and maximal compact spaces. J. Austral. Math. Soc.3, 167–171 (1963).
R. F. Snipes, Convergence and continuity. The adequacy of filterbases, the indequacy of sequences, and spaces in which sequences suffice. Niew Arch. Wiskunde (3)23, 8–31 (1975).
T.Soundararajan, Weakly Hausdorff spaces and the cardinality of topological spaces. In: General Topology and its Rel. to Mod. Analysis and Algebra, Proc. Kanpur Topol. Conf. 1968, pp. 301–306. New York-London 1971 [Math. Reviews44, 976 (1972)].
H. Tong, Minimal bicompact spaces. Bull. Amer. Math. Soc.54, 478–479 (1948).
R. Vaidyanathaswamy, Treatise on Set Topology. Ind. Math. Soc. Madras11947. New York: Chelsea21960, repr. 1964.
R. M. Vogt, Convenient categories of topological spaces for homotopy theory. Arch. Math.22, 545–555 (1971).
A. Wilansky, BetweenT 1 andT 2. Amer. Math. Monthly74, 261–266 (1967).
A. Wilansky, Life withoutT 2. Amer. Math. Monthly77, 157–161 (1970). Correction, ibid77, 728 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hoffmann, RE. On weak Hausdorff spaces. Arch. Math 32, 487–504 (1979). https://doi.org/10.1007/BF01238530
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01238530