On the extension of equalities in connected topological groups
Jan Mycielski (1957)
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Jan Mycielski (1957)
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J. de Groot, T. Dekker (1954-1956)
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Jan Mycielski (1958)
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Andrzej Mostowski (1961)
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Jan Mycielski (1958)
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P. A. Zalesskii (1999)
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Stanisław Hartman, Jan Mycielski (1958)
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The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.