Finitely generated module - Wikipedia

Finitely generated module - Wikipedia: "A finitely generated module over a field is simply a finite-dimensional vector space, and a finitely generated module over the integers is simply a finitely generated abelian group.
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Direct sum of modules - Wikipedia

Direct sum of modules - Wikipedia: "The subspace V × {0} of V ⊕ W is isomorphic to V and is often identified with V; similarly for {0} × W and W. (See internal direct sum below.) With this identification, every element of V ⊕ W can be written in one and only one way as the sum of an element of V and an element of W. The dimension of V ⊕ W is equal to the sum of the dimensions of V and W. One elementary use is the reconstruction of a finite vector space from any subspace W and its orthogonal complement:
{\displaystyle \mathbb {R} ^{n}=W\oplus W^{\perp }}
This construction readily generalises to any finite number of vector spaces."



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Metrization theorem - Wikipedia

Metrization theorem - Wikipedia: "metrizable"



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Tangent bundle - Wikipedia

Tangent bundle - Wikipedia: "One of the main roles of the tangent bundle is to provide a domain and range for the derivative of a smooth function. Namely, if f : M → N is a smooth function, with M and N smooth manifolds, its derivative is a smooth function Df : TM → TN.

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Mapbox - Wikipedia

Mapbox - Wikipedia: "Mapbox is a large provider of custom online maps for websites such as Foursquare, Pinterest, Evernote, the Financial Times, The Weather Channel and Uber Technologies.[2] Since 2010, it has rapidly expanded the niche of custom maps, as a response to the limited choice offered by map providers such as Google Maps and OpenStreetMap.[2] Mapbox is the creator of, or a significant contributor to some open source mapping libraries and applications, including the MBTiles specification, the TileMill cartography IDE, the Leaflet JavaScript library, and the CartoCSS map styling language and parser.
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Klein bottle - Wikipedia

Klein bottle - Wikipedia: "Like the Möbius strip, the Klein bottle is a two-dimensional manifold which is not orientable. Unlike the Möbius strip, the Klein bottle is a closed manifold, meaning it is a compact manifold without boundary. While the Möbius strip can be embedded in three-dimensional Euclidean space R3, the Klein bottle cannot. It can be embedded in R4, however.
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Sinistral and dextral - Wikipedia

Sinistral and dextral - Wikipedia: "Chirality, however, is observer-independent: no matter how one looks at a right-hand screw thread, it remains different from a left-hand screw thread."



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