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On generalized ordered spaces

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Rozprawy Matematyczne tom/nr w serii: 89 wydano: 1971
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EN

1. Introduction................................................................................................................5
2. Characterization of generalized ordered spaces ..............................................7
3. Technical lemmas ..................................................................................................9
4. Paracompactness in GO spaces..........................................................................11
5. Metrizability and related properties in GO spaces.............................................17
6. Local compactness and the Σ-space property in GO spaces.........................23
7. Examples...................................................................................................................28
Bibliography ..................................................................................................................31
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Seria
Rozprawy Matematyczne tom/nr w serii: 89
Liczba stron
32
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Opis fizyczny
Dissertationes Mathematicae, Tom LXXXIX
Daty
wydano
1971
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autor
Bibliografia
  • [1] Arhangel'skiĭ, A. V. On a class of spaces containing all metric and all locally bicompact spaces, Soviet Math. Dokl. 4 (1963), pp. 1051-1055.
  • [2] C. E. Aull, Topological spaces with a a-point finite base, Proc. Amer. Math. Soc. 29 (1971), pp. 411-416.
  • [3] B. J. Ball, Countable paracompactness in linearly ordered spaces, Proc. Amer. Math. Soc. 5 (1954), pp. 190-192.
  • [4] B. J. Ball, The normality of the product of two ordered spaces, Duke Math. Journ. 24 (1957), pp. 15-18.
  • [5] H. R. Bennett, Quasi - developable spaces, Dissertation, Arizona State University, Tempe, Ariz., 1968.
  • [6] H. R. Bennett, A note on point-countability in linearly ordered spaces, Proc. Amer. Math. Soc. 28 (1971), pp. 598-606.
  • [7] R. Bing, Metrization of topological spaces, Canad. Journ. Math. 3 (1951), pp. 175-186.
  • [8] D. K. Burke, On subparacompact spaces, Proc. Amer. Math. Soc. 23 (1969), pp. 655-663.
  • [9] E. Čech, Topological Spaces, Academia (Czechoslovak Acad. Sci.), Prague 1966.
  • [10] Gr. Crecde, Semistratifiable spaces and a factorization of a metrization theorem due to Bing, Dissertation, Arizona State University, Tempe, Ariz., 1968.
  • [11] Gr. Crecde, Concerning semi-stratifiable spaces, Pacific Journ. Math. 32 (1970), pp. 47-54.
  • [12] V. V. Fedorčuk, Ordered sets and the product of topological spaces, Vestnik Moskov Univ. Ser. I Mat. Meh. 21 (1966), 4, pp. 66-71 (Russian) (= Math. Rev. 34 (1967), 640).
  • [13] L. Gillman, and M. Henriksen, Concerning rings of continuous functions, Trans. Amer. Math. Soc. 77 (1954), pp. 340-362.
  • [14] I. Hayashi, The normality of the product of two linearly ordered spaces, Proc. Japan Acad. 43 (1967), pp. 300-304.
  • [15] R. W. Heath, Arc-wise connectedness in semi-metric spaces, Pacific Journ. Math. 12 (1962), pp. 1301-1319.
  • [16] D. J. Lutzer, A metrization theorem for linearly orderable spaces, Proc. Amer. Math. Soc. 22 (1969), pp. 557-558.
  • [17] D. J. Lutzer, and H. R. Bennett, Separability, the countable chain condition and the Lindelöf property in linearly orderable spaces, Proc. Amer. Math. Soc. 23 (1969), pp. 664-667.
  • [18] E. Michael, Point finite and locally finite coverings, Canad. Journ. Math. 7 (1955), pp. 275-279.
  • [19] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), pp. 375-376.
  • [20] E. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Composito Math. 23 (1971), pp. 199-214.
  • [21] K. Nagami, Paracompactness and strong screenability, Nagoya Math. Journ. 8 (1955), pp. 83-88.
  • [22] K. Nagami, Σ-spaces, Fund. Math. 65 (1969), pp. 169-192.
  • [23] K. Nagami, σ-spaces and product spaces, Math. Ann. 181 (1969), pp. 109-118.
  • [24] J-I. Nagata, Modern General Topology, New York 1968.
  • [25] N. Noble, Products with closed projections II, to appear.
  • [26] L. A. Steen, A direct proof that the interval topology is collectionwise normal, Proc. Amer. Math. Soc. 24 (1970), pp. 727-728.
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