
	Where results make sense

Topic: Bijective map

Related Topics

Road map for peace

linear maps

texture mapping

conformal map

map projection

Tube map

logistic map

mind maps

map mathematics

covering map

perceptual maps

In the News (Mon 21 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Open and closed maps - Wikipedia, the free encyclopedia
		In fact, a bijective continuous map is a homeomorphism iff it's open, or equivalently, iff it's closed.
		The inverse of a bijective continuous map is a bijective open/closed map (and vice-versa).
		In complex analysis, the identically named open mapping theorem states that every non-constant holomorphic function defined on a connected open subset of the complex plane is an open map.
	en.wikipedia.org /wiki/Open_map (692 words)

	Group action - Wikipedia, the free encyclopedia
		From these two axioms, it follows that for every g in G, the function which maps x in X to g·x is a bijective map from X to X.
		The image of this map is the orbit of x and the coimage is the set of all left cosets of G
		If such a function f is bijective, then its inverse is also a morphism, and we call f an isomorphism and the two G-sets X and Y are called isomorphic; for all practical purposes, they are indistinguishable in this case.
	en.wikipedia.org /wiki/Effectively (2196 words)

	Bijective Partial Map
		In this case, it is useful to map unique cities to unique integer ids, compute the least-cost tour as a string of integers, and then recover the original city names using the inverse mapping from integers back to cities.
		To compute the inverse, however, the mapping function must be one-to-one so that the mapping is bijective on the partial domains.
		This project explores design trade-offs and alternatives germaine to implementing the abstract data type Bijective Partial Map, which is modeled by a bijective partial function.
	www.cse.ohio-state.edu /europa/projects/0001 (393 words)

	[No title]
		Y : Y --> \R^{162} is a bijective linear map, i.e., that the degrees of freedom on Y are "unisolvent".
		This map is surjective because rdiv : V --> W is surjective.
		Y : Y --> \R^{162} is bijective iff F x f : V --> \R^{162} x \R^{48} = \R^{210} is. Fixing the basis of monomials of V, we identify V with \R^{210} and identify F x f with a linear map \R^{210} --> \R^{210}.
	www.math.umn.edu /~adams/elasticity.txt (730 words)

	The Mandala Centre - BIAES - bijective padding
		The basic idea of bijective padding is to create a bijective map between two sets of files with differing granularity.
		Then, a bijective map between the two sets could be created by connecting objects with the same number.
		Firstly it bijectively maps from the set of all 8-bit granular files, to the set of all 128-bit granular files excluding the null file.
	www.mandala.co.uk /biaes/bijective (617 words)

	Local homeomorphism (Site not responding. Last check: 2007-10-08)
		In topology, a local homeomorphism is a map from one topological space to another that respects locally the topological structure of the two spaces.
		All covering maps are local homeomorphisms; in particular, the universal cover p : C → X of a space X is a local homeomorphism.
		A bijective local homeomorphism is therefore a homeomorphism.
	www.free-download-soft.com /info/error-fixer.html (427 words)

	Isomorphism - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-08)
		In mathematics, an isomorphism is a kind of interesting mapping between objects.
		The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures.
		Formally, an isomorphism is a bijective map f such that both f and its inverse f
	encyclopedia.learnthis.info /i/is/isomorphism.html (278 words)

	Euclidean Isometries (Site not responding. Last check: 2007-10-08)
		An isometry is a bijective map from the plane onto itself that leaves distance and angles invariant.
		For example, the map may shift the points 4 units along the x-axis, -87 units along the y-axis, or along a diagonal ray, say 5 units in the x direction and 2 units in the y direction.
		Given any line in the plane, the mapping translates the points a given number of units in the direction parallel to the line.
	www.geom.uiuc.edu /~crobles/hyperbolic/eucl/isom (306 words)

	[No title]
		The sign map is well-defined because it is a standard result that if sigma is any permutation (of any set), and if sigma is equal to the composition of k transpositions and is also equal to the composition of m transpositions, then (-1)^k = (-1)^m.
		The kernel of the sign map is the alternating group, A_n; that is, A_n is the group of even permutations on n objects.
		The cardinality of the set of left cosets of H is called the index of H in G and is denoted by G:H. Given a in G, h mapsto ah defines a bijective map from H into aH.
	www.math.harvard.edu /~knill/sofia/data/group.txt (4457 words)

	[ref] 29 Mappings
		A zero mapping is a total general mapping that maps each element of its source to the zero element of its range.
		For two general mappings with same source, range, preimage, and image, the sum is defined pointwise, i.e., the images of a point under the sum is the set of all sums with first summand in the images of the first general mapping and second summand in the images of the second general mapping.
		Mappings that are defined on a group and respect multiplication and inverses are group homomorphisms.
	www.math.colostate.edu /WWWextra/manuals/gap/CHAP029.htm (2064 words)

	IDA: Prerequisites
		The map g is the inverse of f and is usually denoted by f
		A map f : A -> B (`the map f from A to B') assigns to each element a of A a unique element f(a) of B.
		The kernel of the linear map f is the linear subspace (of V)
	www.win.tue.nl /ida/demo/voorkenn.html (2804 words)

	[No title]
		The centralizer of f is the loop space of the component containing f of the mapping space of unpointed maps, denoted by map(BX; BY)f.
		Hence the map qff : BX ____-B(Z=C(Z)) is null homotopic.
		In fact, a map BX ____-map(BY; BZ)f induces a pairing BX x BY ____-BZ, and one of its axes is contained in f ?(BX; BZ).
	hopf.math.purdue.edu /Ishiguro/pairing.txt (2796 words)

	[No title]
		If $\mapdef{c}{U(1)}{U(1)}$ is the map defined such that \[c(z) = z^2,\] prove that $c(z_1) = c(z_2)$ iff either $z_2 = z_1$ or $z_2 = -z_1$, and thus that $c$ induces a bijective map $\mapdef{\hli{c}}{\rprospac{1}}{S^1}$.
		The {\it stereographic projection map\/} $\mapdef{\sigma_N}{(S^2 - \{N\})}{\reals^2}$ is defined as follows: For every point $M\not= N$ on $S^2$, the point $\sigma_N(M)$ is the intersection of the line through $N$ and $M$ and the plane of equation $z = 0$.
		\medskip Prove that the map $\s{H}$ induces an injective map from the projective plane onto $\s{H}(S^2)$, and that it is a homeomorphism.
	www.cis.upenn.edu /~cis610/cis61005hw2 (2033 words)

	Padding and Bijection
		It does appear that until recently there were zero bijective schemes for mapping a n-byte file to a file which is a multiple of the block size of an orthodox block cypher.
		Another point is although Matts code is 1-1 (unadulterated bijective whatever) It does not mean that one byte of plaintext maps to one byte of cipher test.
		But they suck in that they are not bijective to the orignal files iencrypted and a false key is very likely to lead to a file that could not be encrypted with the set of rules.
	www.ciphersbyritter.com /NEWS6/PADDING.HTM (14688 words)

	Algebraic Topology: Topology
		A map or continuous function from a topological space (X,OX) to a topological space (Y,OY) is a function from X to Y such that the preimage of any member of OY is a member of OX.
		A homeomorphism is a bijective map of which the inverse is a map, too.
		Also, there need not be any non-constant maps from [0,1] to a connected topological space (indeed, there exist countable connected Hausdorff spaces), and in such a case all path-components are singletons.
	www.win.tue.nl /~aeb/at/algtop-2.html (1509 words)

	[No title]
		Then a model for E_ß is given by the to both side infinite mapping telescope of f1 with the Kv oOE1Z action, for which Z acts by shifting to the right and k 2 Kv acts on the part belonging to n 2 Z by multiplication with OEn1(k).
		It is analogous to the Teichmüller space of a surface w* ith the action of the mapping* class group of the surface.
		The kernel of this map is denoted by eRC(Mi).
	hopf.math.purdue.edu /Lueck/lueck_classifyingspaces1203.txt (13567 words)

	Continuity and Homeomorphisms - Wikibooks
		is a homeomorphism if it is bijective, continuous, and has a continuous inverse.
		Note that a map may be bijective and continuous, but not a homeomorphism.
		, mapping the points in the domain onto the unit circle in the plane.
	en.wikibooks.org /wiki/Continuity_and_Homeomorphisms (157 words)

	Supplement3
		Some meaning can be made of this question by assuming that the concept of "having the same number of elements as" is equivalent to that of a one-to-one or bijective correspondence.
		This notion is reasonable, since if S and T are in bijective correspondence, then each element of S is associated to a unique element of T, and vice versa.
		For example, cl({1,2,3}) consists of all sets in bijective correspondence with {1,2,3}, which are those sets with three elements.
	bradley.bradley.edu /~delgado/404/Schroeder-Bernstein.html (679 words)

	Diffeomorphism
		Given two differentiable manifolds M and N, a bijective map from M to N is called a diffeomorphism if both and its inverse are smooth.
		A differentiable bijection is not necessarily a diffeomorphism, e.g.
		Then the conditions says that the map from to is a diffeomorphism as in the definition above (whenever it makes sense).
	www.brainyencyclopedia.com /encyclopedia/d/di/diffeomorphism.html (414 words)

	Fomalising lexical relations: Lexicon as a relation between sets
		Figure 2.1: Two sets are mapped onto each other by the map f X is the set of terms/words, Y is the set of concepts/properties
		A map in itself does not help solving problems existing in lexicography (such as polysemy, synonymy, etc).
		If is an injective and surjective map, it is a bijective map; in such a case a lexicon could be called onomasiological and semasiological which results in a higher value of the available information.
	coral.lili.uni-bielefeld.de /~ttrippel/datr/node18.html (308 words)

	Physics Help and Math Help - Physics Forums - homeomorphism
		So as you can map the surface of a sphere with apoint missing onto a plane, the two spaces are homeomorphic.
		02-08-2005 04:23 PM here is the first interesting question in topology: prove that a continuous map from the unit disc to the plane, that sends the unit circle identically onto itself, must send some point of the disc to the origin.
		this generalizes to 2 dimensions, the old intermediate value theorem, that a continuous map from the closed unit interval to the line, which sends the end points 0 and 1, to numbers of opposite sign, must send some point of the open unit interval to zero.
	www.physicsforums.com /printthread.php?t=57989 (778 words)

	[No title]
		The bijections used are far from unique - all that is needed is to find one, though.
		The most important distinction we usually need to make on the size of a set (after the distinction between finite and infinite sets) is between those which have the cardinality of the integers or a finite set and those which do not.
		Now define a map $h:B\rightarrow A$ by $$h(b)=\min\{n\;:\; f(a_n)=b\}$$ We know that $h$ is defined for all $b\in B$ because $f$ is onto.
	www.math.unl.edu /~webnotes/src/classes-1995/classAppA.wfy (2382 words)

	Math 428: Topics in Complex Analysis, Fall 98
		Show that T has the structure of a Riemann surface so that the projection map taking a complex number z to its ~ equivalence class is holomorphic.
		Show this projection map is bijective on the open unit square {s + t i : 0
		Show that S has the structure of a Riemann surface so that the projection map taking a complex number z to its # equivalence class is holomorphic.
	math.rice.edu /~hardt/428 (1647 words)

	Francesca Dalla Volta - Interessi di ricerca
		If G is a group, a bijective map f:G -->G is "complete" if the map g so defined: g(x)=xf(x), is bijective.
		It is immediately verified that the identity map is a complete map for a finite group of odd order.
		In 1955 Hall and Paige proved the 2-Sylow subgroups of a finite admissible group are not cyclic, and they conjectured that also the viceversa is true (that is, if the Sylow 2-subgroups of G are not cyclic, G is admissible).
	www.matapp.unimib.it /~dallavolta/ricerca.html (513 words)

	ipedia.com: Group action Article (Site not responding. Last check: 2007-10-08)
		This is formalized by the notion of a group action : every element of the group "acts" like a bijective map on some set.
		Sym(X), where Sym(X) denotes the group of all bijective maps from X to X.
		There is a natural bijection between the set of all left cosets of the subgroup G
	www.ipedia.com /group_action.html (1535 words)

	[No title]
		\vspace {0.25cm}\noindent {\bf Problem B5 (30).} (i) Prove that the {\it Veronese map\/} $\mapdef{V_2}{\reals^3}{\reals^6}$ defined such that \[V_2(x, y, z) = (x^2,\, y^2,\, z^2,\, yz,\, zx,\, xy)\] induces a homeomorphism of $\rprospac{2}$ onto $V_2(S^2)$.
		\medskip (ii) Prove that the {\it Veronese map\/} $\mapdef{V_3}{\reals^4}{\reals^{10}}$ defined such that \[V_3(x, y, z, t) = (x^2,\, y^2,\, z^2,\, t^2,\, xy,\, yz,\, xz,\, xt,\, yt,\, zt)\] induces a homeomorphism of $\rprospac{3}$ onto $V_3(S^3)$.
		You may use a cubic spline curve in the appropriate space, and either use quaternion interpolation, or the exponential map and Rodrigues' formula.
	www.cis.upenn.edu /~cis610/cis70004hw1 (1362 words)

	AMCA: Ultrasubadditive Separating Maps by Edward Beckenstein (Site not responding. Last check: 2007-10-08)
		If H is a linear, bijective, biseparating map, then the realcompactifications of X and Y are homeomorphic; if X and Y are realcompact, then H is a weighted composition map, a map of the form Hf(y) = w(y) f(h(y)) for any f
		In this article we investigate what happens when the continuous functions take values in a non-Archimedean valued field and H is an ultrasubadditive separating map, i.e., H is separating and
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/c/l/86.htm (210 words)

Try your search on: Qwika (all wikis)