Topology

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/topology

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the core principle?Study of properties of spaces invariant under homeomorphisms
2. What is the founding problem?Euler's Seven Bridges of Königsberg problem (1736)
3. Why do mathematicians call topology "rubber‑sheet geometry"?Because it studies shapes that can be stretched or bent like rubber, but not torn or glued, and focuses on properties that stay the same.
4. How many holes does a donut have?A donut, or torus, has one hole, while a sphere has none and a double‑torus has two.

Topology: The mathematical study of properties of space that are preserved under continuous deformations.
Homeomorphism: A continuous deformation mapping one topological space onto another, preserving topological properties.
Topological Invariant: A property of a topological space that remains unchanged under homeomorphisms.
Manifold: A topological space that locally resembles Euclidean space.