$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
FullPage
result
concepts
hypothesis
implications
proof

Continuity of Combinations of Functions

Let $A\subseteq\mathbb{R}^n$, $T\subseteq\mathbb{R}^m$, $f:A\to T$, and $g:T\to \mathbb{R}^{l}$. If $f$ is continous at $\vec{a}\in A$ and $g$ is continuous at $f(\vec{a})\in T$, then $g\circ f$ is continuous at $\vec{a}$

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon. We use sequential characterization of continuity.

Continuity of Combinations of Functions

Let $A\subseteq\mathbb{R}^n$, $T\subseteq\mathbb{R}^m$, $f:A\to T$, and $g:T\to \mathbb{R}^{l}$. If $f$ is continous at $\vec{a}\in A$ and $g$ is continuous at $f(\vec{a})\in T$, then $g\circ f$ is continuous at $\vec{a}$

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon. We use sequential characterization of continuity.
FullPage
result
concepts
hypothesis
implications
proof
FullPage
result
concepts
hypothesis
implications
proof

Continuity of Combinations of Functions

Let $A\subseteq\mathbb{R}^n$, $T\subseteq\mathbb{R}^m$, $f:A\to T$, and $g:T\to \mathbb{R}^{l}$. If $f$ is continous at $\vec{a}\in A$ and $g$ is continuous at $f(\vec{a})\in T$, then $g\circ f$ is continuous at $\vec{a}$

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon. We use sequential characterization of continuity.

Continuity of Combinations of Functions

Let $A\subseteq\mathbb{R}^n$, $T\subseteq\mathbb{R}^m$, $f:A\to T$, and $g:T\to \mathbb{R}^{l}$. If $f$ is continous at $\vec{a}\in A$ and $g$ is continuous at $f(\vec{a})\in T$, then $g\circ f$ is continuous at $\vec{a}$

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon. We use sequential characterization of continuity.
FullPage
result
concepts
hypothesis
implications
proof