Construct · 3 fields · 3 citations
One name. Different field. Different construct. One map.
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In topology, the fiber of a continuous map over a point is the preimage of that point (the slice of the total space lying above it) and a fiber bundle is a space that looks locally like a product of a base space with a fixed typical fiber, glued together by a structure group. Steenrod's The topology of fibre bundles is the foundational treatment of how these local products are assembled into a global object. The referent is a geometric-algebraic structure built from preimages, with no connection to a strand of glass or a dietary component beyond the shared image of threads lying side by side.[1]
In optics an optical fiber is a thin strand of glass or plastic that confines and guides light along its length by total internal reflection, carrying signals over long distances with low loss. Kao and Hockham's 1966 Dielectric-fibre surface waveguides for optical frequencies argued that purified glass fibres could serve as a practical optical waveguide, the insight that launched fibre-optic communications. The referent is a physical waveguide for light, an entirely different thing from a topological preimage or an indigestible plant component.[2]
In nutrition, dietary fiber is the part of plant food that the human small intestine cannot digest or absorb, passing largely intact into the large bowel where it affects transit, bulk, and fermentation. Trowell's 1976 Definition of dietary fiber and hypotheses that it is a protective factor in certain diseases set out a working definition and proposed its protective role against several Western diseases. The referent is a class of indigestible plant polysaccharides and lignin in the diet, unrelated to a light-guiding glass thread or a topological fiber.[3]
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