Equivalence of continuity definitions
12107
How is the epsilon-delta definition of continuity equivalent to the following statement?
98666
Continuity defined for rational and irrational numbers
153952
A map between metric spaces preserving convergent sequences is continuous
127114
Differentiability implying continuity
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
133265
Definition of continuity at a point
59859
Locally Lipschitz implies continuity. Does the converse implication hold?
60700
Continuity of a function to the integers
121957
Is $p\mapsto \|f\|_p$ continuous?
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
141366
Absolutely continuity and Lipschitz-like continuity
95327
Lipschitz and uniform continuity
135661
Weakly continuous operators are continuous
60383
What is the intuition for the point-set topology definition of continuity?
97975
Does factor-wise continuity imply continuity?
33289
Negation of definition of continuity