# Connected space: Quiz

Question 1: This result can be considered a generalization of the ________.
Connected spaceIntermediate value theoremContinuous functionReal number

Question 2: Any ________ over a connected field is connected.
Hilbert spaceTopological vector spaceLocally convex topological vector spaceFréchet space

Question 3: A path-component of X is an equivalence class of X under the ________ defined by x is equivalent to y if there is a path from x to y.
Equivalence relationGroup actionGroup (mathematics)Binary relation

Question 4: There are stronger forms of connectedness for a ________.
Metric spaceTopological spaceCompact spaceHausdorff space

Question 5: Since a simply connected space is by definition, also required to be ________, any simply connected space is also connected.
TopologyConnected spaceManifoldTopological space

Question 6: Every ________ is locally path-connected.
GeometryDifferentiable manifoldManifoldDifferential geometry

Question 7: In topology and related branches of ________, a connected space is a topological space which cannot be represented as the union of two or more disjoint nonempty open subsets.
GeometryAlgebraMathematical logicMathematics

Question 8: More generally, any ________ is locally path-connected.
Differentiable manifoldLocally compact spaceTopological propertyTopological manifold

Question 9: The spectrum of a commutative ________ is connected.
Nakayama lemmaRing (mathematics)Commutative ringLocal ring

Question 10: Connectedness is one of the principal ________ that is used to distinguish topological spaces.
Trivial topologyTopologyNormal spaceTopological property