Nuprl Definition : m-ptwise-cont
PtwiseCONT(f:X ⟶ Y) ==
∀x:X. ∀k:ℕ+. ∃delta:{d:ℝ| r0 < d} . ∀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
FDL editor aliases :
m-ptwise-cont
Latex:
PtwiseCONT(f:X {}\mrightarrow{} Y) ==
\mforall{}x:X. \mforall{}k:\mBbbN{}\msupplus{}.
\mexists{}delta:\{d:\mBbbR{}| r0 < d\} . \mforall{}y:X. ((mdist(dx;x;y) \mleq{} delta) {}\mRightarrow{} (mdist(dy;f x;f y) \mleq{} (r1/r(k))))
Date html generated:
2020_05_20-AM-11_48_07
Last ObjectModification:
2019_11_08-AM-09_59_38
Theory : reals
Home
Index