New posts in continuity

Is the inverse of a continuous bijective function also continuous? [duplicate]

continuity inverse

Prob. 23, Chap. 4 in Baby Rudin: Every convex function is continuous and every increasing convex function of a convex function is convex

real-analysis analysis continuity convex-analysis uniform-continuity

A function that satisfies the Intermediate Value Theorem and takes each value only finitely many times is continuous.

calculus real-analysis analysis continuity

Splitting a continuous monotonically-increasing function $f(x)$ as $h(x)+h(x+\epsilon) = f(x)$

real-analysis continuity monotone-functions

What does it mean if a map corresponds to a path?

Metric space and continuity

real-analysis convergence-divergence metric-spaces continuity

Proving that $\sup_{s \in [a,b)}f(s)=\sup_{s \in [a,b)\cap \mathbb{Q}}f(s)$ for right continuous function.

real-analysis continuity supremum-and-infimum

French Railroad Metric/Topology

continuity metric-spaces

Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$

real-analysis continuity

Must a continuous and periodic functions have a smallest period?

real-analysis continuity periodic-functions

Discontinuous functionals on infinite dimensional topological vector space [closed]

functional-analysis continuity topological-vector-spaces

Continuity of an "SVD" operator

calculus linear-algebra continuity matrix-calculus svd

Consider $Y = \mathbb{N} \cup \{ \infty\}$ and $X = \{ \frac{1}{n}\mid n \in \Bbb N\} \cup \{0\}$

continuity metric-spaces

Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.

real-analysis continuity

Proving the existence of a point with a certain property for a continuous function

calculus integration functions continuity

Must compact bijections be continuous?

real-analysis general-topology continuity metric-spaces compactness

Is it possible to have a function differentiable but not continuous in a given interval?

derivatives continuity

For which conditions on countable sets does continuity implies uniform continuity

real-analysis continuity uniform-continuity

Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

real-analysis measure-theory continuity examples-counterexamples

Show Continuity Using Epsilon Delta Definition [closed]

calculus continuity