Topological monoids of monotone injective partial selfmaps of ℕ with cofinite domain and image
2011 ◽
Vol 48
(3)
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pp. 342-353
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Keyword(s):
In this paper we study the semigroup ℐ ∞↗ (ℕ) of partial cofinal monotone bijective transformations of the set of positive integers ℕ. We show that the semigroup ℐ ∞↗ (ℕ) has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology τ on ℐ ∞↗ (ℕ) such that (ℐ ∞↗ (ℕ); τ) is a topological inverse semigroup, is discrete. Finally, we describe the closure of (ℐ ∞↗ (ℕ); τ) in a topological semigroup.
1978 ◽
Vol 19
(1)
◽
pp. 59-65
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Keyword(s):
1977 ◽
Vol 18
(2)
◽
pp. 199-207
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1990 ◽
Vol 33
(1)
◽
pp. 159-164
2005 ◽
Vol 4
(1)
◽
pp. 135-173
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1973 ◽
Vol 18
(4)
◽
pp. 299-306
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1978 ◽
Vol 84
(2)
◽
pp. 323-336
◽
2010 ◽
Vol 2010
◽
pp. 1-13
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1990 ◽
Vol 42
(2)
◽
pp. 335-348
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Keyword(s):