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The Convergence in Topological Linear Space

Zhou Hexun (Henan University)  
In this paper,we study some properties of convergence in Topologicpl Linear Space (TPS)by introducing a new topological Conslfructure of TPS. Wediscuss the relations between the Weak Convergence and σ(Y) Convergence and obtain a equivalent form of weak couvergence,it is that Weak topologic can be founded by taking all set of form {x∈X: |g(Tx)|ε, T∈B[X,Y],g∈Y} aslocalneighborhood subbase.
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