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Being a continuous compact single-valued mapping of a locally finite polyhedron with non-zero Euler-Poincaré characteristic, (rhocirc scirc fcirc r Prightarrow Chookrightarrow P) has a fixed point (p_{W}=(rho circ scirc fcirc r)(p_{W} inrho(W[sGamma(V[r(p_{W})])])).
Similar(59)
Then (T: P to P) is a continuous, compact operator.
Suppose that (A:overline{U}rightarrow C) is a continuous, compact map.
Then (T: P to P) is a continuous, compact, and increasing operator.
Then T ϵ η is a continuous compact operator from [ 0, 1 ] × L ∞ ( Q T ) to L ∞ ( Q T ).
Suppose that (U overline{V} rightarrow E_{1}) is a continuous, compact (that is, (U overline{V})) is a relatively compact subset of (E_{1})) map.
Suppose that (mathcal{U}:overline{V}to E_{1}) is a continuous, compact (that is, (mathcal{U} overline{V})) is a relatively compact subset of (E_{1})) map.
Suppose that (mathcal{F}:overline{U}to C) is a continuous, compact (that is, (mathcal{F} overline{U})) is a relatively compact subset of C) map.
Suppose that (F:overline{U}rightarrow C) is a continuous, compact (that is, (F overline{U})) is a relatively compact subset of C) map.
Suppose that (F:overline{X}to C) is a continuous, compact (that is, (F overline {X})) is a relatively compact subset of C) map.
Suppose that (mathcal{U}:overline{V}longrightarrow E_{1} ) is a continuous, compact (that is, (mathcal{U} overline{V})) is a relatively compact subset of (E_{1} )) map.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com