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Best Sets of Lecture Notes and Articles

Overview of basic results about images and preimages

Intuition of the meaning of homology groups

Are "if" and "iff" interchangeable in definitions?

Difference between gradient and Jacobian

$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed

Why do we use a Least Squares fit?

Cardinality of Borel sigma algebra

Dot Product Intuition

Is there really no way to integrate $e^{-x^2}$?

Lebesgue measurable but not Borel measurable

Difference between topology and sigma-algebra axioms.

What is difference between cycle, path and circuit in Graph Theory

Interpretation of limsup-liminf of sets

Lebesgue measurable set that is not a Borel measurable set

What is the intuition for the point-set topology definition of continuity?

Examples of uncountable sets with zero Lebesgue measure

Is there a $\sigma$-algebra on $\mathbb{R}$ strictly between the Borel and Lebesgue algebras?

Topologist's sine curve is not path-connected

An intuitive idea about fundamental group of $\mathbb{RP}^2$

Are Singleton sets in $\mathbb{R}$ both closed and open?

Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly

Is there any difference between $P$ and $\Pr$ to represent probabilities?

What is the difference between topological and metric spaces?

Rigorous proof that $dx dy=r\ dr\ d\theta$

Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?

Why do we need (the abstract concept of) random variables (in discrete probability models)?

Set of points at which sequence of measurable functions converge (another approach)

Why do we use dummy variables in integrals?

Cantor set: Lebesgue measure and uncountability