Notes to my Cat---Path Connected implies Connected, an elegant proof.
... Fundamental group and Homotopy as Natural Transformation
Beyond Sequences: A Topological Approach to Density Arguments
Representable functor in Calculus
Proving Homeomorphism with Yoneda Lemma: The Unification of epsilon-delta and epsilon-N Formulation
Commutative Algebra and Algebraic Geometry (4): Zariski topology on affine scheme
Commutative Algebra and Algebraic Geometry (5): Spectrum of Boolean ring and Stone Duality.
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