Connected Sets Quiz

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| By Thames
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Thames
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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 12 | Questions: 15 | Updated: Dec 12, 2025
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Question 1 / 16
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1) Every interval in ℝ is connected.

Explanation

Intervals have no gaps.

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About This Quiz
Connected Sets Quiz - Quiz

Ready to build a solid understanding of connectedness? This quiz introduces you to what it means for a set to be connected—that it cannot be split into two nonempty, disjoint open sets. You’ll explore connectedness through intervals in ℝ, unions of sets, and behavior in general topological spaces. Through these... see morequestions, you’ll learn how connected sets behave, how intersections influence connectedness, and why intervals are the fundamental connected sets in ℝ. By the end, you’ll be ready to identify connected sets and explain why certain sets break apart into disconnected pieces.
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2)
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2) The union of two connected sets is always connected.

Explanation

Only guaranteed if they intersect.

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3) A connected set in ℝ is always an interval.

Explanation

Connected subsets of ℝ are intervals.

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4) The empty set is considered connected.

Explanation

∅ has no separation.

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5) Singleton sets in any topological space are connected.

Explanation

One-point sets cannot be separated.

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6) Which set is connected in ℝ?

Explanation

Only [0,2] is an interval.

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7) Which property is necessary for a set to be connected?

Explanation

Definition of connectedness.

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8) The set (−∞,0) ∪ (0,∞) in ℝ is:

Explanation

There is a gap at 0.

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9) Which statement is true?

Explanation

Only intervals result in connectedness.

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10) Let A=[0,1], B=[1,2]. Then A∪B is:

Explanation

They touch at 1 → [0,2].

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11) Which sets are connected?

Explanation

Intervals only.

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12) Which statements are correct?

Explanation

Connectedness is topological; open intervals connected.

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13) When is A∪B connected?

Explanation

Intersection ensures connection.

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14) Examples of connected sets:

Explanation

Intervals and singletons.

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15) A set in ℝ is connected if it cannot be expressed as the union of two nonempty, disjoint open sets.

Explanation

This is the definition of connectedness.

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Every interval in ℝ is connected.
The union of two connected sets is always connected.
A connected set in ℝ is always an interval.
The empty set is considered connected.
Singleton sets in any topological space are connected.
Which set is connected in ℝ?
Which property is necessary for a set to be connected?
The set (−∞,0) ∪ (0,∞) in ℝ is:
Which statement is true?
Let A=[0,1], B=[1,2]. Then A∪B is:
Which sets are connected?
Which statements are correct?
When is A∪B connected?
Examples of connected sets:
A set in ℝ is connected if it cannot be expressed as the union of...
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