Disconnected Sets Quiz

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| By Thames
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Thames
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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 15 | Updated: Dec 1, 2025
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1) A subset (A ⊂ R) is disconnected if:

Explanation

Disconnected means split into two nonempty, disjoint open subsets.

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About This Quiz
Disconnected Sets Quiz - Quiz

Ready to understand how and why sets break apart? This quiz introduces you to disconnected sets—sets that can be separated into two nonempty, disjoint open subsets in the subspace topology. You’ll analyze examples in ℝ and ℝ², determine which sets split into multiple components, and explore how disconnectedness behaves unde... see moreunions, complements, and closures. Through these problems, you’ll build a strong intuition for how sets become separated and why intervals remain connected. By the end, you’ll confidently identify disconnected sets and explain the structural properties that cause them to fall apart. see less

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2) Which set is disconnected in R?

Explanation

Gap.

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3) If X is disconnected, which true?

Explanation

Definition.

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4) Which interval not disconnected?

Explanation

[0,3] interval.

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5) Empty set is:

Explanation

Convention.

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6) A={x∈R: x^2≤1 or x^2≥4}:

Explanation

Multiple pieces.

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7) X⊂R^n disconnected if exist nonempty U,V:

Explanation

Definition.

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8) Select disconnected:

Explanation

Separated or finite >1.

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9) Which true for disconn sets?

Explanation

True.

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10) Disconnected examples:

Explanation

Gaps.

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11) If X disconnected, operations produce disconnected:

Explanation

Complement splits.

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12) Disconnected in R2:

Explanation

A,D disconnect.

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13) X disconnected if:

Explanation

Charact.

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14) True for disconn X:

Explanation

Properties.

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15) True about disconn sets:

Explanation

Correct.

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A subset (A ⊂ R) is disconnected if:
Which set is disconnected in R?
If X is disconnected, which true?
Which interval not disconnected?
Empty set is:
A={x∈R: x^2≤1 or x^2≥4}:
X⊂R^n disconnected if exist nonempty U,V:
Select disconnected:
Which true for disconn sets?
Disconnected examples:
If X disconnected, operations produce disconnected:
Disconnected in R2:
X disconnected if:
True for disconn X:
True about disconn sets:
Alert!

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