Abstract
This chapter develops several models of topological spaces associated to collections of measurements.
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Notes
- 1.
The term map will be used as shorthand for “continuous function” throughout the book.
- 2.
An embedding is an injective continuous map \(f:X\rightarrow Y\) whose image \(f(X)\) is homeomorphic to its domain \(X\).
- 3.
The elements of \(A\) are need not be ordered themselves.
- 4.
A space is Hausdorff if every two distinct points are contained in disjoint open neighborhoods.
- 5.
A space is paracompact if every open cover \(\fancyscript{U}\) has a locally finite open refinement cover \(\fancyscript{V}\) in which each element \(V\in \fancyscript{V}\) is a subset of some \(U\in \fancyscript{U}\).
- 6.
A perturbation is a small change to a mathematical object.
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Robinson, M. (2014). Parametrization. In: Topological Signal Processing. Mathematical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36104-3_2
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DOI: https://doi.org/10.1007/978-3-642-36104-3_2
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