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condensation; weaker connected topology; Luzin space
It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of $\aleph_1$ copies of the Cantor set consistently does not condense onto a connected compact space. This answers two questions from [2].
[1] Gruenhage G.: Partitions of compact Hausdorff spaces. Fund. Math. 142 (1993), 89-100. MR 1207473 | Zbl 0814.54015
[2] Tkačenko M.G., Tkachuk V.V., Uspenskij V.V., Wilson R.G.: In quest of weaker connected topologies. Comment. Math. Univ. Carolinae 37.4 (1996), 825-841. MR 1440714
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