The Mackey problem for free locally convex spaces
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Abstract It is known that the free locally convex space {L(X)} on a space X is metrizable only if X is finite and that {L(X)} is barrelled if and only if X is discrete. We significantly generalize these results by proving that {L(X)} is a Mackey space if and only if X is discrete. Noting that real locally convex spaces which are Mackey groups are always Mackey spaces, but that the converse is false, it is also proved here that {L(X)} is a Mackey group if and only if it is a Mackey space.
2014 ◽
Vol 57
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pp. 803-809
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2002 ◽
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1967 ◽
Vol 15
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pp. 295-296
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1980 ◽
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pp. 331-337
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1985 ◽
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1983 ◽
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2020 ◽
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2010 ◽
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pp. 299-310
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1971 ◽
Vol 70
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pp. 399-400
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