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Path Connectedness Quizzes, Questions & Answers

Top Trending Path Connectedness Quizzes

Ready to apply path connectedness to real problem-solving? This quiz explores geometric reasoning, curve parameterization, and structural analysis to determine when sets in ℝ and ℝ² remain path connected....

Questions: 15 | Attempts: 11 | Last updated: Dec 12, 2025

Sample Question 1
Let A = {(x,y) ∈ ℝ² : y = x²}. Which reasoning correctly proves A is path connected?

It is bounded.

It is the image of a continuous function t ↦ (t,t²)

It is symmetric about the y-axis.

It contains the origin.

Sample Question 2
Suppose X ⊆ ℝ² is such that any two points can be joined by a piecewise-linear path inside X. Then:

X is arc connected

X is path connected

X is convex

X must be open

Sample Question 3
Let B = ℝ² ∖ {(0,y): y ≤ 0}. Why is B path connected?

Removing a point never breaks path connectedness

Removing a ray in the plane does not disconnect it

The set is convex

It is homeomorphic to a closed disk

Recent Path Connectedness Quizzes

Path Connectedness Proof Strategies Quiz

Think you can prove a set is path connected? This quiz challenges you to use formal strategies such as constructing explicit paths, using convexity, leveraging intersections, and applying continuous images of intervals....

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
To prove a space X is path connected, it is enough to show that for any two points x, y ∈ X there exists a continuous map f : [0,1] → X with f(0)=x and f(1)=y.

True

False

Path Connectedness Quiz

Ready to understand one of the most intuitive forms of connectedness? This quiz introduces you to path connectedness—the idea that any two points in a space can be joined by a continuous path. You’ll examine...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
Every path connected space is connected.

True

False