How We Write Topology Assignments That Actually Hold Together
Topology assignments don't fail because students don't know results. They fail because proofs lose clarity midway. A definition is applied too quickly. A step is assumed instead of explained. Our process is built to prevent exactly that.
1. Understanding the Question Before Writing Anything
We start by reading the question carefully, sometimes more than once. Many topology problems look simple but hide strict requirements. We identify what must be shown, which definitions are required, and where examiners usually expect justification.
2. Laying Out Definitions and Known Results Clearly
Before proving anything, we set the groundwork. Definitions are written explicitly, not implied. Relevant theorems are introduced at the right moment, so the proof feels guided instead of rushed.
3. Building the Proof Step by Step
Each step is written so it follows naturally from the previous one. No jumps. No hidden assumptions. If a conclusion depends on a definition, that connection is explained clearly.
4. Explaining Why Each Step Works
This is where many students lose marks. We explain not just what is done, but why it is valid. That explanation turns a correct proof into a convincing one.
5. Final Review for Logic and Readability
Before delivery, the entire solution is reread from an examiner's point of view. If a step feels unclear on first reading, it is rewritten until the logic feels smooth.
