That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and...That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.展开更多
Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.展开更多
文摘That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.
基金Project supported by NSF (10171034) of ChinaNSF (970395) of Guangdong province
文摘Let G be a graph which contains exactly one simple closed curve.We prove that a continuous map f:G→G has zero topological entropy if and only if there exist at most k■[(Edg(G)+End(G)+ 3)/2]different odd numbers n_1,...,n_k such that Per(f)is contained in ∪_i^k=1 ∪_j~∞=0 n_i2~j,where Edg(G) is the number of edges of G and End(G)is the number of end points of G.
