Nuprl Definition : m-unif-cont
UC(f:X ⟶ Y) == ∀k:ℕ+. ∃delta:{d:ℝ| r0 < d} . ∀x,y:X. ((mdist(dx;x;y) ≤ delta) ⇒ (mdist(dy;f x;f y) ≤ (r1/r(k))))
Definitions occuring in Statement :
mdist: mdist(d;x;y),
rdiv: (x/y),
rleq: x ≤ y,
rless: x < y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
natural_number: $n
Definitions occuring in definition :
int-to-real: r(n),
natural_number: $n,
rdiv: (x/y),
apply: f a,
mdist: mdist(d;x;y),
rleq: x ≤ y,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rless: x < y,
real: ℝ,
set: {x:A| B[x]} ,
exists: ∃x:A. B[x],
nat_plus: ℕ+
FDL editor aliases :
m-unif-cont
m-unif-cont
m-unif-cont
Latex:
UC(f:X {}\mrightarrow{} Y) ==
\mforall{}k:\mBbbN{}\msupplus{}. \mexists{}delta:\{d:\mBbbR{}| r0 < d\} . \mforall{}x,y:X. ((mdist(dx;x;y) \mleq{} delta) {}\mRightarrow{} (mdist(dy;f x;f y) \mleq{} (r1/r(k)))\000C)
Date html generated:
2019_10_30-AM-06_35_47
Last ObjectModification:
2019_10_25-PM-01_19_08
Theory : reals
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