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Register a new userUnconditionally tau-Closed and tau-Algebraic Sets in Groups
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Authors
Olga V. Sipacheva
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Families of unconditionally $tau$-closed and $tau$-algebraic sets in a group are defined, which are natural generalizations of unconditionally closed and algebraic sets defined by Markov. A sufficient condition for the coincidence of these families is found. In particular, it is proved that these families coincide in any group of cardinality at most $tau$. This result generalizes both Markovs theorem on the coincidence of unconditionally closed and algebraic sets in a countable group (as is known, they may be different in an uncountable group) and Podewskis theorem on the topologizablity of any ungebunden group.
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