On group uniformities on the square of a space and extending pseudometrics
1995 ◽
Vol 51
(2)
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pp. 309-335
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We give some conditions under which, for a given pair (d1, d2) of continuous pseudometrics respectively on X and X3, there exists a continuous semi-norm N on the free topological group F(X) such that N(x · y−1) = d1(x, y) and N(x · y · t−1 · z−1) ≥ d2((x, y), (z, t)) for all x, y, z, t ∈ X. The “extension” results are applied to characterise thin subsets of free topological groups and obtain some relationships between natural uniformities on X2 and those induced by the group uniformities *V, V* and *V* of F(X).
1993 ◽
Vol 114
(3)
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pp. 439-442
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1975 ◽
Vol 13
(1)
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pp. 121-127
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Keyword(s):
1969 ◽
Vol 1
(2)
◽
pp. 145-160
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1973 ◽
Vol 9
(1)
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pp. 83-88
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1971 ◽
Vol 4
(1)
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pp. 17-29
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1973 ◽
Vol 16
(2)
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pp. 220-227
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Keyword(s):
1988 ◽
Vol 44
(2)
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pp. 252-258
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1970 ◽
Vol 2
(2)
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pp. 165-178
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Keyword(s):
1986 ◽
Vol 33
(1)
◽
pp. 103-112
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