Topologist%27s sine curve is not path connected

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Dec 09, 2013 · The path to such a theory was paved by Lorentz in the year 1904. He showed, that by a suitable transformation of time and coordinates, the influence of uniform motion upon the optics of moving systems in Maxwell 's equations, is vanishing, and that all observations known up to then, are in agreement with the additional consequences of this new ...
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A curve is an arched or bent shape, like the curve of a smiling mouth or the curve of a road that twists and turns as you drive along the coast.
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Dec 25, 2009 · The topologist's sine curve is not path-connected: There is no path connecting the origin to any other point on the space. The topologist's sine curve is connected: All nonzero points are in the same connected component, so the only way it could be disconnected is if the origin and the rest of the space were the two connected components.
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The curves are the radially mapping points for the third iterate of the section map (solid) and the images of these points (dotted). These curves are distorted by their proximity to the 1:1 islands shown in figure 4.17. The corresponding section is shown in figure 4.19. Exercise 4.7: Computing the Poincaré–Birkhoff construction
can't be path-connected. Using this fact, one can show that the Topologist's sine curve as defined by Munkres is also not path-connected; see this stackexchange answer. The path to success tends to be innovating truly new offerings, not just applying digital lipstick on your existing offerings. This is a mind-set shift that a lot of incumbents struggle with. Sean Brown: How and where do these digital leaders make their bolder moves?
File.openAsString(path) - Opens a text file and returns the contents as a string. Displays a file open dialog box if path is an empty string. Use lines=split(str," ") to convert the string to an array of lines. See also: File.openUrlAsString. File.openAsRawString(path) - Opens a file and returns up to the first 5,000 bytes as a string. Returns ...
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