Test Topology Note

Introduction to topological spaces

Goals

In this note, we establish:

  1. First goal
  2. Second goal
  3. Third goal
Notation

Throughout this note, we adopt the following conventions:

  • denotes the set of real numbers
  • Additional notation as needed

First Section

Definition: Name of Definition

Let be … We say that is … if …

Remark

Brief commentary or intuition about the definition above.

Main Results

Theorem: Name of Theorem

Statement of the theorem.

Proof

Proof goes here.

Therefore the result follows.

Example

Consider the case where … Then:

Further Results

Lemma: Name of Lemma

Statement of a supporting result.

Proof

Proof of the lemma.

Theorem: Main Theorem

Statement that uses the lemma above.

Proof

By the lemma, …


Further Reading

  • Author, A. Title of Book, Chapter N (Year)
  • Author, B. Title of Book, Chapter M (Year)