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Norms on Free Topological Groups
Author(s) -
Bicknell Kevin,
Morris Sidney A.
Publication year - 1978
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/10.3.280
Subject(s) - mathematics , topological group , hausdorff space , combinatorics , norm (philosophy) , free group , free product , identity function , discrete mathematics , group (periodic table) , topology (electrical circuits) , physics , quantum mechanics , political science , law
A norm on a group G is a function N mapping G into the set of non‐negative real numbers such that for each x and y in G , N ( xy −1 ) ⩽ N ( x )+ N ( y ) and N ( e ) = 0, where e is the identity element of G . It is shown here that if F ( X ) is the free topological group on any completely regular Hausdorff space X and H is a subgroup of F ( X ) generated by a finite subset of X , then any norm on H can be extended to a continuous norm on F ( X ).
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