nh x 1

nh xTrong ton hc, nh x l khi qut ca khi nim hm s. Hm s li xut pht t khi nim tng quan gia cci lng vt l. Chng hn trong mt chuyn ng u, di qung ng i c bng tch ca tc vi thigian. Nu tc l 5m/s th qung ng i c trong t giy l s = 5t.V ngha, nh x biu din mt tng quan (quan h) gia cc phn t ca hai tp hp X v Y tho mn iu kin:mi phn t x ca tp X u c mt v ch mt phn t tng ng vi n. Quan h tho mn tnh cht nycng c gi l quan h hm, v th khi nim nh x v hm l tng ng nhau. Khi nim hm ni trn l khinim hm n tr, n cho php vi mi x ch c mt y duy nht tng ng vi x. Tuy nhin trong l thuyt hm, cbit l l thuyt xc sut, hm cn c th bao hm cc hm a tr, trong mt gi tr x c th tng ng vi mt sgi tr ca y.Bi ny ch vit v cc nh x (hm) n tr.

Cc thut ngTrong cc sch gio khoa ton trung hc c s v trung hc ph thng thng nh ngha:

nh x f t mt tp hp X vo mt tp hp Y (k hiu ) l mt quy tc cho mi phn t x Xtng ng vi mt phn t xc nh y Y, phn t y c gi l nh ca phn t x, k hiu .Tp X c gi l tp ngun, tp Y c gi l tp ch.

Vi mi , tp con ca X gm cc phn t, c nh qua nh x f bng y, c gi l to nh ca phn ty qua f, k hiu l

Vi mi tp con , tp con ca Y gm cc phn t l nh ca qua nh x f c gi l nhca tp A k hiu l f(A)

Vi mi tp con , tp con ca X gm cc phn t x c nh c gi l to nh ca tpB k hiu l

Mt nh ngha khc, dng trong l thuyt tp hp, sau khi nh ngha khi nim quan h, ngi ta nh ngha:Mt nh x t tp X vo tp Y l mt quan h t X vo Y tho mn iu kin: mi phn t u c quan h vi mt v ch mt phn t .Vit di dng mnh , nh x , k hiu , l mt quan h tho mn:

1. ;2.

Nu X v Y l cc tp hp s th nh x c gi l hm s. Khi X cng c gi l tp xc nhhay min xc nh ca hm s f(x),tp cc nh f(X) c gi l min gi tr ca hm f(x).

nh x 2

Vi tnh cht c bn nh ca mt tp hp rng l mt tp hp rng

A = nh ca tp hp con l tp hp con ca nh

nh ca phn giao nm trong giao ca phn nhf(A B) f(A) f(B)

nh ca phn hp l hp ca cc phn nhf(A B) = f(A) f(B)

Ton nh, n nh v song nh

Ton nh l nh x t X vo Y trong nh ca X l ton b tphp Y. Khi ngi ta cng gi f l nh x t X ln Y

hay

n nh l nh x khi cc phn t khc nhau ca X cho cc nh khc nhau trong Y .n nh cn c gi l nhx 1-1 v tnh cht ny.

hay

Song nh l nh x va l n nh, va l ton nh. Song nh va l nh x 1-1 v va l nh x "onto" (t X lnY) .

nh x 3

Mt s nh x c bit nh x khng i (nh x hng): l nh x t X vo Y sao cho mi phn t x X u cho nh ti mt phn t

duy nht Y. nh x ng nht: l nh x t X vo chnh X sao cho vi mi phn t x trong X, ta c f(x)=x. nh x nhng: l nh x f t tp con vo Y cho f(x)= x vi mi . Khi ta k hiu f : X

Y. Mt quan nim khc v nh x nhng l: nu l n nh, khi xem f ch l nh x t X vo tpcon , f s l song nh. Lc ta c tng ng 1-1 gia X vi f(X) nn c th thay th cc phn tca tp con bng cc phn t ca tp X. Vic ny c gi l nhng X vo Y bng n nh f.123

nh x tch v nh x ngc nh x tch

Cho hai nh x v . Tch ca hai nh x f, g, k hiu l l nh x t X voZ, xc nh bi ng thc:

Mt s tnh cht ca nh x tch

Nu l n nh th f l n nh.Nu l ton nh th g l ton nh.Nu l song nh th f v g u l song nh.

nh x ngc (Inverse map)

Cho nh x , nu c nh x sao cho

th g c gi l nh x ngc, hay nghch o ca f, k hiu l .nh x f c nh x ngc khi v ch khi f l song nh.

Cc khi nim nh x khc (dch t ting anh) nh x x nh Canonical map nh x chnh tc Classifying map nh x phn loi Conformal map nh x bo gic: nh x bo ton ln ca cc gc, ngha l gc gia cc tip tuyn vi hai

ng cong bt k (ti giao im ca chng) bng gc gia cc tip tuyn vi cc nh ca hai ng (ti giaoim tng ng)

Constant map nh x khng i Contiguous map nh x tip ln Continuous map nh x lin tc: [1]

nh x f t x0 X ln Y sao cho vi mi ln cn W ca f(x0) u tn ti ln cn V ca x0 trong X (V X)sao cho f(V) W c gi l nh x lin tc ti x0 ln Y

nh x Y = f(X) c gi l nh x lin tc t X vo Y nu n lin tc vi mi x X nh x ng phi: f:XY l nh x song nh, lin tc v nh x ngc cng lin tc. Khi X v Y c

gi l hai khng gian, hai tp hp ng phi hay tng ng t p [1] Contour map Phng nh cc ng nm ngang Equivariant map nh x ng bin Evaluation map nh x nh gi

nh x 4

Excission map nh x ct Fibre map nh x phn th, nh x cc khng gian phn th Identification map nh x ng nht ho Inclusion map nh x nhng chm Interior map nh x trong Involutory map nh x i hp Light map nh x chun gin on (khp ni c cc im gin on) Lowering map nh x h thp Regular map nh x chnh quy Shrinking map nh x co rt hay nh x co l nh x ca khng gian mtric vo chnh n, sao cho khong cch

gia hai im bt k b gim i qua nh x . Ngi ta chng minh rng, nu khng gian mtric l th mi nhx co bao gi cng c mt v ch mt im bt ng x, tc l F(x) = x

Simplicial map nh x n hnh Tensor map nh x tenx Affine mapping nh x afin Analytic mapping nh x gii tch Bicontinuous mapping nh x song lin tc Chain mapping nh x chui, nh x dy chuyn Closed mapping nh x ng: f:XY c gi l nh x ng nu vi mi tp A ng X u c f(A) l tp

ng trong Y [1] Open mapping nh x m: f:XY c gi l nh x m nu vi mi tp A m X u c f(A) l tp m

trong Y [1] Diferentiable mapping nh x kh vi Epimorphic mapping nh x ton hnh Homomorphous mapping nh x ng cu Homotopic mapping nh x dy chuyn ng lun Isometric mapping nh x ng cc Isotonic mapping nh x bo ton th t Linear mapping nh x tuyn tnh Meromorphic mapping nh x phn hnh Monomorphic mapping nh x n cu Monotone mapping nh x n iu Non-alternating mapping nh x khng thay phin Norm-preserving mapping nh x bo ton chun One-to-one mapping nh x mt-mt, hai chiu, (song nh) Perturbation mapping nh x lch Preclosed mapping nh x tin ng Pseudoconformal mapping nh x gi bo gic Quasi-conformal mapping nh x ta bo gic Quasi-open mapping nh x ta m Rational mapping nh x hu t Sense-preserving mapping nh x bo ton chiu Slit mapping nh x ln min c lt ct trong Starlike mapping nh x hnh sao Symplectic mapping nh x i ngu ximplectic Topological mapping nh x t p Univalent mapping nh x n dip

nh x 5

Lin kt Bi ging ti trng i hc Cn Th [2]

Bi ging v Khng gian x nh v nh x x nh [3]

Cc ch chnh trong ton hc

Nn tng ton hc | i s | Gii tch | Hnh hc | L thuyt s | Ton hc ri rc | Ton hc ng dng|

Ton hc gii tr | Ton hc t p | Xc sut thng k

Ch thch[1] http:/ / www. ctu. edu. vn/ coursewares/ supham/ topodaicuong/ chuong2. htm#VIII[2] http:/ / www. ctu. edu. vn/ coursewares/ supham/ topodaicuong/ chuong1. htm#II[3] http:/ / www. ctu. edu. vn/ coursewares/ supham/ hhxaanh/ chuong1c. htm

Ngun v ngi ng gp vo bi 6

Ngun v ngi ng gp vo binh x Ngun: http://vi.wikipedia.org/w/index.php?oldid=4553178 Ngi ng gp: -

Ngun, giy php, v ngi ng gp vo hnhTp tin:Anh_xa.JPG Ngun: http://vi.wikipedia.org/w/index.php?title=Tp_tin:Anh_xa.JPG Giy php: GNU Free Documentation License Ngi ng gp: -

Giy phpCreative Commons Attribution-Share Alike 3.0 Unportedhttp:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/

nh xCc thut ngVi tnh cht c bnTon nh, n nh v song nhMt s nh x c bitnh x tch v nh x ngcCc khi nim nh x khc (dch t ting anh)Lin kt

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