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Another example of a pullback comes from the theory of fiber bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the category of topological spaces with continuous maps) X × B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles.
This linear map is known as the pullback (by ), and is frequently denoted by . More generally, any covariant tensor field – in particular any differential form – on N {\displaystyle N} may be pulled back to M {\displaystyle M} using ϕ {\displaystyle \phi } .
Office Open XML (OOXML) format was introduced with Microsoft Office 2007 and became the default format of Microsoft Word ever since. Pertaining file extensions include:.docx – Word document.docm – Word macro-enabled document; same as docx, but may contain macros and scripts.dotx – Word template
The pullback bundle is an example that bridges the notion of a pullback as precomposition, and the notion of a pullback as a Cartesian square. In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in the base space at which they are anchored: the ...
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In mathematics, a pullback bundle or induced bundle [1] [2] [3] is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B and a continuous map f : B′ → B one can define a "pullback" of E by f as a bundle f * E over B′. The fiber of f * E over a point b′ in B′ is just the fiber of E over f(b′).
Annotated information flow diagram. An information flow diagram (IFD) is a diagram that shows how information is communicated (or "flows") from a source to a receiver or target (e.g. A→C), through some medium. [1]: 36–39 The medium acts as a bridge, a means of transmitting the information. Examples of media include word of mouth, radio ...
ConceptDraw DIAGRAM can import both generations of MS Visio stencils (VSS or VSSX) ConceptDraw DIAGRAM supports the round-trip import and export of the Microsoft Visio 2003 - 2016 file format that is used for MS Visio documents (VSD, VDX, and VSDX formats). ConceptDraw DIAGRAM can import both generations of MS Visio stencils (VSS or VSSX).