How does this definition of continuity involving open sets work?
12107
How is the epsilon-delta definition of continuity equivalent to the following statement?
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
132946
Continuous and bounded imply uniform continuity?
98666
Continuity defined for rational and irrational numbers
133265
Definition of continuity at a point
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
127900
Interior of closure of open set in topological space
76351
Equivalence of continuity definitions
45395
Difference between continuity and uniform continuity
59519
What about the continuity of these functions in the uniform topology?
60700
Continuity of a function to the integers
33289
Negation of definition of continuity
69283
The limit points of an open interval (open set)
9614
How does the existence of a limit imply that a function is uniformly continuous
53627
Proving continuity of $f$
83831
Continuity based on restricted continuity of two subsets
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??