The space can be divided into regions, each of which is a small piece of a product space - but the space as a whole may be twisted in all sorts of ways that would be impossible for a true product space.įor example, what's the difference between a cylinder and a mobius strip? They're both formed by taking a square, and joining opposite edges. So what is a fiber bundle, and why should we care? It's something that looks almost like a product of two topological spaces. Interesting things that you can do in a manifold because of that property of being locallyĪ fiber bundle is based on a similar sort of idea: a local property that does not necessarily hold globally - but instead the local property being a property of individual points, it's based on a property of regions of the space. Topological space where every point is inside of a neighborhood that appears to beĮuclidean, but the space as a whole may be very non-euclidean. The idea of a fiber bundle is very similar to the idea of a manifold. Geeky pun in there, but it's too pathetic to explain.) I like to say that a fiber bundle is a cross between a product and a manifold. For instance, today, I'm going to talk about something called a fiber bundle. Rest assured - there's plenty more topology It's been a while since I've written a topology post.
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