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I asked the question. However, I think I have a simpler example than the currently accepted answer.
Let $X=(1,0)$ and $Y=(0,1)$ be the constant unit vector fields in the $x$ and $y$ directions. Define a connection such that:
$$\begin{matrix}\nabla_XX=\hat\jmath&\nabla_XY=-\hat\imath\\
\nabla_YX=0&...
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In mathematics, particularly in the area of functional analysis and topological vector spaces, the vague topology is an example of the weak-* topology which arises in the study of measures on locally compact Hausdorff spaces.
Let X be a locally compact Hausdorff space. Let M(X) be the space of complex Radon measures on X, and C0(X)* denote the dual of C0(X), the Banach space of complex continuous functions on X vanishing at infinity equipped with the uniform norm. By the Riesz representation theorem M(X) is isometric to C0(X)*. The isometry maps a measure μ to a linear functional
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Relevance is the concept of one topic being connected to another topic in a way that makes it useful to consider the second topic when considering the first. The concept of relevance is studied in many different fields, including cognitive sciences, logic, and library and information science. Most fundamentally, however, it is studied in epistemology (the theory of knowledge). Different theories of knowledge have different implications for what is considered relevant and these fundamental views have implications for all other fields as well.
== Definition ==
"Something (A) is relevant to a task...
