In mathematics, specifically algebraic topology, the mapping cylinder of a continuous function f {\displaystyle f} between topological spaces X {\displaystyle...

called the mapping fiber. The mapping cone can be understood to be a mapping cylinder M f {\displaystyle Mf} with the initial end of the cylinder collapsed...

natural map. The mapping cylinder of f is by definition the mapping cone of g. This complex is called the cone in analogy to the mapping cone (topology)...

an associated topological space M f {\displaystyle Mf} called the mapping cylinder of f {\displaystyle f} . There is a canonical subspace embedding i...

are mapped to horizontal lines. The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's...

between different units of measurement CHS conversion of data storage, mapping cylinder/head/sector tuples to linear base address CPS conversion, in computer...

glue X and Y together along their common subspace. Quotient space Mapping cylinder Stephen Willard, General Topology, (1970) Addison-Wesley Publishing...

connected Universal cover Monodromy Homotopy lifting property Mapping cylinder Mapping cone (topology) Wedge sum Smash product Adjunction space Cohomotopy...

[perpendicular] to the axis, together with the cylinder of the same base, is equal to that right cylinder of which the base is the latus versum (that is...

online mapping services still exclusively use the Web Mercator. The Mercator projection can be visualized as the result of wrapping a cylinder tightly...

Cylinder-head-sector (CHS) is an early method for giving addresses to each physical block of data on a hard disk drive. It is a 3D-coordinate system made...

accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize...

one. The homotopy fiber is dual to the mapping cone, much as the mapping path space is dual to the mapping cylinder. Given a topological space X {\displaystyle...

colimitpg 4-8 is a generalization of homotopy pushouts, such as the mapping cylinder used to define a cofibration. This notion is motivated by the following...

M\times (-\varepsilon ,\varepsilon )} . If M {\displaystyle M} has a mapping cylinder neighbourhood N = C φ {\displaystyle N=C_{\varphi }} of some map φ...

projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator....

(A mapping path space satisfies the universal property that is dual to that of a mapping cylinder, which is a push-out. Because of this, a mapping path...

neighborhood deformation retract; that is, X {\displaystyle X} contains a mapping cylinder neighborhood of a closed subspace A {\displaystyle A} and f {\displaystyle...

theorem mapping 1.   The mapping cone (or cofiber) of a map ƒ:X→Y is C f = Y ∪ f C X {\displaystyle C_{f}=Y\cup _{f}CX} . 2.  The mapping cylinder of a map...

The equirectangular projection (also called the equidistant cylindrical projection or la carte parallélogrammatique projection), and which includes the...

This is a list of some of the most commonly used coordinate transformations. Let ( x , y ) {\displaystyle (x,y)} be the standard Cartesian coordinates...

y)=(t-k,f^{k}(y)),} for each k ∈ Z and for each (t,y) ∈ R × N. The mapping cylinder of f is defined to be the Cr manifold M f = ( R × N ) / ∼ f . {\displaystyle...

mapped to perpendicular lines). The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's...

area of the cylinder minus its caps. This result would eventually lead to the Lambert cylindrical equal-area projection, a way of mapping the world that...

to be simplicial complexes. Furthermore, X will be replaced by the mapping cylinder of the inclusion A → X. This will not change anything as SP is a homotopy...

but not a fibration. More generally, the projection Mf → I of the mapping cylinder of a map f: X → Y between connected CW complexes onto the unit interval...

and History of web mapping. Aerial photography and satellite imagery have provided high-accuracy, high-throughput methods for mapping physical features...

In geometry and topology, trivial cylinders are certain pseudoholomorphic curves appearing in certain cylindrical manifolds. In Floer homology and its...

issues. Overlapping ATA CHS mapping with BIOS CHS mapping produced the lowest common denominator of 10:4:6 bits, or 1024 cylinders, 16 heads, and 63 sectors...

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of...