![]() ![]() ![]() In particular, I give the details of the construction of the physical Hilbert space. That result was obtained in the case where the set K was bounded. Pseudo-Hermitian quantum mechanics with unbounded metric operators. The conditions under which these spaces have a flnite cardinality are found. It is proved that all tangent spaces are complete. Finally in Section 5 we study complete metric spaces. To investigate the asymptotic behavior of (X, d) at infinity, one can consider a sequence of rescaling metric spaces (X, 1 rn d). Ascoli-Arezela theorem, which characterizes compact sets in the space of continuous functions, is established in Section 4. More precisely, we establish the following result, which generalizes the corresponding result in Reich and Zaslavski (see also and ). The latter is applied to establish the separability of the space of continuous functions when the underlying space is compact. In this paper we study the asymptotic behavior of (unrestricted) infinite products of generic sequences of mappings belonging to the space * and obtain convergence to a unique common fixed point. Since surjective isometries preserve both the metric and. I need to show that all Cauchy sequences are convergent. I need to show that X X is a complete metric space. We consider the topological subspace * ⊂ equipped with the relative topology and the metric d. The definition of a peaking set involves only the norm and the addition operation of the vector space. Let X X be the set of all bounded sequences x (xn) x ( x n) of real numbers and let. Denote by * the closure of the set * in the uniform space. ![]()
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