Intro

In this section, we introduce topological properties of \mathbb{R} such as open and closed sets, compactness, connectedness, etc. This section focuses exclusively on the real line, although all of these properties exist for general topological spaces and discussed in [Topology].

• Open sets

• Closed sets

• Points

• Compactness

• Connected

• Measure

• Density

• Meager sets

• Baires category theorem

• Blumburg Theorem