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On Free Topological Groups with the Inductive Limit Topologies a
Author(s) -
SIPACHEVA OLGA V.
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36812.x
Subject(s) - countable set , mathematics , direct limit , abelian group , limit (mathematics) , topological group , group (periodic table) , limit point , topology (electrical circuits) , set (abstract data type) , free group , pure mathematics , isolated point , discrete mathematics , topological space , combinatorics , topological vector space , mathematical analysis , physics , computer science , quantum mechanics , programming language
Countable spaces with an only nonisolated point for which the free topological groups are the inductive limits of the sets of words having restricted length are characterized. It is proved for a collectionwise normal X that if its free topological group is the inductive limit of the sets of words having restricted length, then any closed discrete set of non‐ P ‐points in X is countable. All the results obtained are valid for both Abelian and non‐Abelian free groups.