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A few remarks on reduced ideal-products. (English) Zbl 0877.54007

Summary: A nicer shape of the condition \((\Lambda\Psi)\) (which ensures preservation of separation axioms \(T_k\), \(k=0,1,2,3,3\frac12\), in reduced ideal-products) is given. If an reduced-ideal product is \(T_0\), \(T_1\) or \(T_2\) then “almost all” coordinate spaces have this property. This implication holds for \(T_3\)-property if the condition \((\Lambda\Psi)\) is satisfied. Some results on mappings and homogenicity of reduced ideal-products are obtained. Finally, it is proved that the reduced ideal product of topological groups (rings) is a topological group (ring).

MSC:

54B10 Product spaces in general topology
54B15 Quotient spaces, decompositions in general topology
03C65 Models of other mathematical theories
54H11 Topological groups (topological aspects)
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