Weak Topology

Name: Weak Topology
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Bol Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, weak topology is an alternative term for initial topology. The term is most commonly used for the initial topology of a normed vector space or topological vector space with respect to its (continuous) dual. The remainder of this article will deal with this case, which is one of the basic concepts of functional analysis. One may call subsets of a topological vector space weakly closed (respectively, compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise, functions are sometimes called weakly continuous (respectively, differentiable, analytic, etc.) if they are continuous (respectively, differentiable, analytic, etc.) with respect to the weak topology.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, weak topology is an alternative term for initial topology. The term is most commonly used for the initial topology of a normed vector space or topological vector space with respect to its (continuous) dual. The remainder of this article will deal with this case, which is one of the basic concepts of functional analysis. One may call subsets of a topological vector space weakly closed (respectively, compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise, functions are sometimes called weakly continuous (respectively, differentiable, analytic, etc.) if they are continuous (respectively, differentiable, analytic, etc.) with respect to the weak topology.

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