Nuprl Definition : ss-homotopic

ss-homotopic(X;x0;x1;a;b) ==
  ∃p:Point(Path(Path(X))). (p@r0 ≡ a ∧ p@r1 ≡ b ∧ (∀t:{t:ℝt ∈ [r0, r1]} (p@t@r0 ≡ x0 ∧ p@t@r1 ≡ x1)))



Definitions occuring in Statement :  path-at: p@t path-ss: Path(X) ss-eq: x ≡ y ss-point: Point(ss) rccint: [l, u] i-member: r ∈ I int-to-real: r(n) real: all: x:A. B[x] exists: x:A. B[x] and: P ∧ Q set: {x:A| B[x]}  natural_number: $n
Definitions occuring in definition :  exists: x:A. B[x] ss-point: Point(ss) path-ss: Path(X) all: x:A. B[x] set: {x:A| B[x]}  real: i-member: r ∈ I rccint: [l, u] and: P ∧ Q ss-eq: x ≡ y path-at: p@t int-to-real: r(n) natural_number: $n
FDL editor aliases :  ss-homotopic

Latex:
ss-homotopic(X;x0;x1;a;b)  ==
    \mexists{}p:Point(Path(Path(X)))
      (p@r0  \mequiv{}  a  \mwedge{}  p@r1  \mequiv{}  b  \mwedge{}  (\mforall{}t:\{t:\mBbbR{}|  t  \mmember{}  [r0,  r1]\}  .  (p@t@r0  \mequiv{}  x0  \mwedge{}  p@t@r1  \mequiv{}  x1)))



Date html generated: 2020_05_20-PM-01_20_31
Last ObjectModification: 2018_07_05-PM-03_50_49

Theory : intuitionistic!topology


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