Abstract
We prove that an irresolvable left topological group is of the first category. The pseudocharacter of an irresolvable left topological groupG is countable, provided thatG is Abelian or its cardinality is nonmeasurable. Some other cardinal invariants of an irresolvable left topological group are also determined.
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References
W. W. Comfort and J. van Mill, “Groups with only resolvable group topologies,”Proc. Amer. Math. Soc.,120, No. 3, 687–696 (1994).
I. V. Protasov, “Resolvability of groups”,Mat. Stud.,9, No. 2, 130–148 (1998).
I. V. Protasov, “Decompositions of direct products of groups”,Ukr. Mat. Zh.,49, No. 10, 1385–1395 (1997).
I. V. Protasov, “Irresolvable topologies on groups”,Ukr. Mat. Zh.,50, No. 12, 1646–1655 (1998).
I. V. Protasov, “Maximal topologies on groups”,Sib. Mat. Zh.,39, No. 6, 1368–1381 (1998).
O. T. Alas, I. V. Protasov, M. G. Tkachenko, V. V. Tkachuk, R. G. Wilson, and I. V. Yaschenko, “Almost all submaximal groups are paracompact and δ-discrete”,Fund. Math.,156, 241–260 (1998).
E. G. El'kin, “Ultrafilters and irresolvable spaces”,Vestn. Mosk. Univ., No. 5, 51–56 (1969).
A. Illanes, “Finite and ω-resolvability,”Proc. Amer. Math. Soc.,124, No. 4, 1243–1246 (1996).
I. V. Protasov, “Resolvability of τ-bounded groups,”Mat. Stud., Issue 5, 17–20 (1995).
I. I. Guran, “On topological groups close to finally compact ones”,Dokl. Akad. Nauk SSSR,256, No. 6, 1305–1307 (1981).
Additional information
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 758–765, June, 2000.
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Protasov, I.V. Irresolvable left topological groups. Ukr Math J 52, 868–875 (2000). https://doi.org/10.1007/BF02591781
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DOI: https://doi.org/10.1007/BF02591781