Geodesic
Linearly ordered space whose square and higher powers cannot be condensed onto a normal space
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 68-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus “very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.
Mots-clés : condensation
Keywords: normality, linearly ordered space, pseudocompact, Cartesian product, monotonically normal, Stone–Cech compactification, Tychonoff plank. 
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     title = {Linearly ordered space whose square and higher powers cannot be condensed onto a normal space},
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O. I. Pavlov. Linearly ordered space whose square and higher powers cannot be condensed onto a normal space. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 68-73. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a6/

[1] Pavlov O., “Condensations of Cartesian products”, Comment. Math. Univ. Carolin., 40:2 (1999), 355–365 | MR | Zbl

[2] Malykhin D. V., “On condensations of topological spaces and products”, Fundamental physics and mathematics problems and modelling of technical and technological systems, 2, “Stankin”, M., 1998, 27–33 (in Russian) | MR

[3] Buzyakova R. Z., “On condensations of Cartesian Products onto normal spaces”, Vestnik of MSU, 51:1 (1996), 13–14 (in Russian)

[4] Yakivchik A. N., “On tightenings of a product of finally compact spaces”, Vestnik of MSU, 44:4 (1989), 86–88 (in Russian)

[5] Heath R. W., Lutzer D. J., Zenor P. L., “Monotonically normal spaces”, Trans. Amer. Math. Soc., 178 (1973), 481–493 | DOI | MR | Zbl

[6] Engelking R., General Topology, Mir, M., 1989 (in Russian) | MR

[7] Stephenson R. M., “k-Compact and related spaces”, Handbook of set-theoretic topology, eds. K. Kunen, J. Vaughan, North-Holland Publishing, Amsterdam, 1984, 603–632 | DOI | MR

[8] Glicksberg I., “Stone–Cech compactifications of products”, Trans. Amer. Math. Soc., 90 (1959), 369–382 | MR | Zbl

[9] Dieudonne J., “Sur les espaces topologiques susceptibles d'etre munis d'une structure uniforme d'espace complet”, C. R. Acad. Sci. Paris, 209 (1939), 666–668 | MR

[10] Przymusinski T. S., “Products of normal spaces”, Handbook of set-theoretic topology, eds. K. Kunen, J. Vaughan, North-Holland Publishing, Amsterdam, 1984, 781–826 | DOI | MR