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  2. Mapping cylinder - Wikipedia

    en.wikipedia.org/wiki/Mapping_cylinder

    Given a map :, the mapping cylinder is a space , together with a cofibration ~: and a surjective homotopy equivalence (indeed, Y is a deformation retract of ), such that the composition equals f. Thus the space Y gets replaced with a homotopy equivalent space M f {\displaystyle M_{f}} , and the map f with a lifted map f ~ {\displaystyle {\tilde ...

  3. Map (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Map_(mathematics)

    A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]

  4. Category:Functions and mappings - Wikipedia

    en.wikipedia.org/.../Category:Functions_and_mappings

    Self-concordant function; Semi-differentiability; Semilinear map; Set function; List of set identities and relations; Shear mapping; Shekel function; Signomial; Similarity invariance; Soboleva modified hyperbolic tangent; Softmax function; Softplus; Splitting lemma (functions) Squeeze theorem; Steiner's calculus problem; Strongly unimodal ...

  5. Bijection, injection and surjection - Wikipedia

    en.wikipedia.org/wiki/Bijection,_injection_and...

    One has always X ⊆ f −1 (f(X)) and f(f −1 (Y)) ⊆ Y, where f(X) is the image of X and f −1 (Y) is the preimage of Y under f. If f is injective, then X = f −1 (f(X)), and if f is surjective, then f(f −1 (Y)) = Y. For every function h : X → Y, one can define a surjection H : X → h(X) : x → h(x) and an injection I : h(X) → Y ...

  6. Geometric function theory - Wikipedia

    en.wikipedia.org/wiki/Geometric_function_theory

    A rectangular grid (top) and its image under a conformal map f (bottom). It is seen that f maps pairs of lines intersecting at 90° to pairs of curves still intersecting at 90°. A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane. More formally, a map,

  7. Function analysis diagram - Wikipedia

    en.wikipedia.org/wiki/Function_analysis_diagram

    A function analysis diagram (FAD) is a method used in engineering design to model and visualize the functions and interactions between components of a system or product. It represents the functional relationships through a diagram consisting of blocks, which represent physical components, and labeled relations/arrows between them, which represent useful or harmful functional interactions.

  8. Bilinear map - Wikipedia

    en.wikipedia.org/wiki/Bilinear_map

    It generalizes to n-ary functions, where the proper term is multilinear. For non-commutative rings R and S, a left R-module M and a right S-module N, a bilinear map is a map B : M × N → T with T an (R, S)-bimodule, and for which any n in N, m ↦ B(m, n) is an R-module homomorphism, and for any m in M, n ↦ B(m, n) is an S-module ...

  9. Karnaugh map - Wikipedia

    en.wikipedia.org/wiki/Karnaugh_map

    A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced it in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] (aka.