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

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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. 
@article{VSGU_2014_10_a6,
     author = {O. I. Pavlov},
     title = {Linearly ordered space whose square and higher powers cannot be condensed onto a normal space},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {68--73},
     publisher = {mathdoc},
     number = {10},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_10_a6/}
}
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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/