Topological Continuity Quizzes, Questions & Answers

Top Trending Topological Continuity Quizzes

How well can you apply the topological definition of continuity? This quiz helps you connect theory to practice by examining preimages of open sets, behavior on basis elements, continuity in discrete and trivial topologies,...

Questions: 15 | Attempts: 12 | Last updated: Jan 27, 2026

Sample Question 1
A function f : X → Y is continuous if:

The preimage of every open set in Y is open in X.

The preimage of every closed set in Y is closed in X.

For each x ∈ X, the function preserves neighborhood structure.

F is injective.

Sample Question 2
If f : X → Y is continuous and U ⊆ Y is open, then:

F⁻¹(U) is open

F⁻¹(U) is closed

F⁻¹(U) may be empty

F⁻¹(U) = X

Topological Continuity Concepts Quiz

Think you understand topological continuity? This quiz explores the formal definition using preimages of open sets and examines how continuity behaves in discrete, trivial, and general topologies. You’ll test your...

Questions: 15 | Attempts: 11 | Last updated: Jan 27, 2026

Sample Question 1
Which of the following is the correct topological definition of continuity of f : X → Y?

Images of open sets are open

Preimages of open sets are open

Images of closed sets are closed

Preimages of compact sets are compact

Sample Question 2
The preimage of an open set under a continuous function is:

Always open

Always closed

Either open or closed

Not defined

Recent Topological Continuity Quizzes

Topological Continuity Quiz

Ready to understand continuity beyond ε–δ definitions? This quiz introduces the topological definition of continuity, where open sets and their preimages determine whether a function is continuous....

Questions: 15 | Attempts: 10 | Last updated: Jan 27, 2026

Sample Question
In topology, a function is continuous if the preimage of every open set is open.

True

False