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Constant function: Quiz

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Question 1: A function on a ________ is locally constant if and only if it is constant.
Connected spaceManifoldTopological spaceTopology

Question 2: In ________, a constant function is a function whose values do not vary and thus are constant.
Mathematical logicMathematicsGeometrySet theory

Question 3: For functions between preordered sets, constant functions are both ________ and order-reversing; conversely, if f is both order-preserving and order-reversing, and if the domain of f is a lattice, then f must be constant.
Function (mathematics)Order theoryDerivativeMonotonic function

Question 4: Constant functions can be characterized with respect to ________ in two ways.
Inverse functionExponentiationFunction compositionFunction (mathematics)

Question 5: The first characterization of constant functions given above, is taken as the motivating and defining property for the more general notion of constant morphism in ________.
Mathematical logicAlgebraic topologyCategory theoryMathematics

Question 6: Every constant function whose domain and codomain are the same is ________.
Function (mathematics)Ring (mathematics)Vector spaceIdempotence

Question 7: Every constant function between ________ is continuous.
Hausdorff spaceTopological spaceMetric spaceCompact space

Question 8: If f is a real-valued function of a real variable, defined on some interval, then f is constant if and only if the ________ of f is everywhere zero.
CalculusDerivativeDifferential calculusIntegral

Question 9: For all functions g, h : CA, f o g = f o h, (where "o" denotes ________).
Inverse functionFunction (mathematics)Function compositionExponentiation

Question 10: In contexts where it is defined, the ________ of a function measures how that function varies with respect to the variation of some argument.
Differential calculusIntegralDerivativeCalculus







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