New posts in continuity

Lipschitz Continuous $\Rightarrow$ Uniformly Continuous

real-analysis continuity solution-verification

Continuity of an inverse function.

Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous

metric-spaces continuity uniform-continuity

How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?

calculus continuity

prove $x \mapsto x^2$ is continuous

functions proof-writing continuity

Handoff with 2011 Mac using El Capitan

macbook-pro macos continuity

Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?

analysis metric-spaces continuity uniform-continuity cauchy-sequences

Is a right-continuous function on a compact space even "uniformly right-continuous"?

real-analysis functional-analysis continuity uniform-continuity stochastic-analysis

How to make continuity and handoff working [iPhone 5S; iOS 8.1][Macbook pro mid 2012]

iphone macbook-pro bluetooth continuity

Is there a monotonic function discontinuous over some dense set?

real-analysis continuity

Do all continuous real-valued functions determine the topology?

general-topology algebraic-topology continuity category-theory manifolds

Characterization of continuity with open subsets.

real-analysis continuity definition

If a function is continuous and differentiable everywhere is the derivative continuous?

real-analysis continuity

For manifolds of the same dimension, are submersions equivalent to immersions?

general-topology geometry differential-geometry continuity manifolds

Can $ f\colon \mathbb{R}^k \to \mathbb{R}^n$ such that $ \forall y \in \operatorname{im}(f)$, $f^{-1}(y) = \{a_y,b_y\} $ be continuous?

real-analysis general-topology continuity

Is there another topology on $\mathbb{R}$ that gives the same continuous functions from $\mathbb{R}$ to $\mathbb{R}$?

general-topology continuity

A function vanishing at infinity is uniformly continuous

calculus real-analysis continuity uniform-continuity

Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$

analysis continuity

Continuous function positive at a point is positive in a neighborhood of that point

analysis continuity