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Supercompact spaces. (English) Zbl 0502.54026

##### MSC:
 54D30 Compactness 54G20 Counterexamples in general topology 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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##### References:
 [1] Bell, M.G., Not all compact spaces are supercompact, General topology appl., 8, 151-155, (1978) · Zbl 0385.54016 [2] Bell, M.G., A cellular constraint in supercompact Hausdorff spaces, Canad. J. math., 30, 1144-1151, (1978) · Zbl 0367.54009 [3] M.G. Bell, A first countable supercompact Hausdorff space with a closed G_δ non-supercompact subspace, Coll. Math. (to appear). · Zbl 0474.54012 [4] Bell, M.G.; van Mill, J., The compactness number of a topological space, Fund. math., 106, 163-173, (1980) · Zbl 0362.54014 [5] Brouwer, A.E.; Schrijver, A., A characterization of supercompactness with an application to treelike spaces, Report mathematical centre ZW 34/74, (1974), Amsterdam · Zbl 0292.54020 [6] E.K. van Douwen, Special bases for compact metrizable spaces, Fund. Math. (to appear). · Zbl 0497.54031 [7] E.K. van Douwen, Transfer of information about β$$N$$−$$N$$ via open remainder maps, Illinois J. Math. (to appear). · Zbl 0709.54020 [8] van Douwen, E.K., Nonsupercompactness and the reduced measure algebra, Comm. math. univ. car., 21, 507-512, (1980) · Zbl 0437.54014 [9] Efimov, B.; Engelking, R., Remarks on dyadic spaces, II, Coll. math., 13, 181-197, (1965) · Zbl 0137.16104 [10] Engelking, R., Cartesian products and dyadic spaces, Fund. math., 57, 287-304, (1965) · Zbl 0173.50603 [11] Engelking, R., On the double circumference of Alexandroff, Bull. acad. polon. sci. Sér. sci. math. astron. phys., 16, 629-634, (1968) · Zbl 0167.21001 [12] Engelking, R.; Pelczyński, A., Remarks on dyadic spaces, Coll. math., 11, 55-63, (1963) · Zbl 0123.15905 [13] Frolík, Z., Nonhomogeneity of βP−P, Comment. math. univ. car., 8, 705-709, (1967) · Zbl 0163.44601 [14] Gillman, L.; Jerison, M., Rings of continuous functions, (1960), Van Nostrand Princeton, NJ · Zbl 0093.30001 [15] de Groot, J., Supercompactness and superextensions, (), 89-90 · Zbl 0191.21202 [16] van Mill, J., A topological characterization of products of compact tree-like spaces, rapport 31, (1975), Wisk. Sem. Vrije Universiteit Amsterdam [17] van Mill, J.; Mills, C.F., On the character of supercompact spaces, Top. proc., 3, 227-236, (1978) · Zbl 0413.54031 [18] van Mill, J.; Mills, C.F., Closed G_δ-subsets of supercompact Hausdorff spaces, Indag. math., 41, 155-162, (1979) · Zbl 0412.54025 [19] Mills, C.F., A simpler proof that compact metrizable spaces are supercompact, Proc. AMS, 73, 388-390, (1979) · Zbl 0401.54018 [20] C.F. Mills, Compact topological groups are supercompact, Fund. Math. (to appear). [21] Mills, C.F.; van Mill, J., A nonsupercompact image of a supercompact space, Houston J. math., 5, 241-247, (1979) · Zbl 0423.54012 [22] Rudin, M.E., Souslin’s conjecture, Amer. math. monthly, 76, 1113-1119, (1969) · Zbl 0187.27302 [23] Rudin, M.E., Lectures on set theoretic topology, () · Zbl 0318.54001 [24] Strok, M.; Szymański, A., Compact metric spaces have binary bases, Fund. math., 89, 81-91, (1975) · Zbl 0316.54030 [25] Verbeek, A., Superextensions of topological spaces, () · Zbl 0256.54014
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