Extensions and new observations of Tychonoff,Stone-Weierstrass theorems,compactifications and the realcompactification |
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Authors: | Hueytzen J Wu |
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Institution: | Department of Mathematics, Texas A & I University, Kingsville, TX 78363, USA |
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Abstract: | An extension of the Tychonoff theorem is obtained in characterizing a compact space by the nets and the images induced by any family of continuous functions on it. The idea of this extension is applied to get a new process and new observations of compactifications and the realcompactification. Finally, a sufficient and necessary condition of a vector sublattice or a subalgebra of C1(X) to be dense in (C1(X),∥·∥) is provided in terms of the nets in X induced by C1(X), where C1(X) is the space of all bounded real continuous functions on a topological space X with pointwise ordering, and ∥·∥ is the supremum norm. |
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Keywords: | Primary 54D30 54D35 54D60 Secondary 54C35 46A40 46J10 |
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