$$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Self-defined math definitions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Math symbol commands \newcommand{\intd}{\,{\rm d}} % Symbol 'd' used in integration, such as 'dx' \newcommand{\diff}{{\rm d}} % Symbol 'd' used in differentiation \newcommand{\Diff}{{\rm D}} % Symbol 'D' used in differentiation \newcommand{\pdiff}{\partial} % Partial derivative \newcommand{DD}[2]{\frac{\diff}{\diff #2}\left( #1 \right)} \newcommand{Dd}[2]{\frac{\diff #1}{\diff #2}} \newcommand{PD}[2]{\frac{\pdiff}{\pdiff #2}\left( #1 \right)} \newcommand{Pd}[2]{\frac{\pdiff #1}{\pdiff #2}} \newcommand{\rme}{{\rm e}} % Exponential e \newcommand{\rmi}{{\rm i}} % Imaginary unit i \newcommand{\rmj}{{\rm j}} % Imaginary unit j \newcommand{\vect}[1]{\boldsymbol{#1}} % Vector typeset in bold and italic \newcommand{\phs}[1]{\dot{#1}} % Scalar phasor \newcommand{\phsvect}[1]{\boldsymbol{\dot{#1}}} % Vector phasor \newcommand{\normvect}{\vect{n}} % Normal vector: n \newcommand{\dform}[1]{\overset{\rightharpoonup}{\boldsymbol{#1}}} % Vector for differential form \newcommand{\cochain}[1]{\overset{\rightharpoonup}{#1}} % Vector for cochain \newcommand{\bigabs}[1]{\bigg\lvert#1\bigg\rvert} % Absolute value (single big vertical bar) \newcommand{\Abs}[1]{\big\lvert#1\big\rvert} % Absolute value (single big vertical bar) \newcommand{\abs}[1]{\lvert#1\rvert} % Absolute value (single vertical bar) \newcommand{\bignorm}[1]{\bigg\lVert#1\bigg\rVert} % Norm (double big vertical bar) \newcommand{\Norm}[1]{\big\lVert#1\big\rVert} % Norm (double big vertical bar) \newcommand{\norm}[1]{\lVert#1\rVert} % Norm (double vertical bar) \newcommand{\ouset}[3]{\overset{#3}{\underset{#2}{#1}}} % over and under set % Super/subscript for column index of a matrix, which is used in tensor analysis. \newcommand{\cscript}[1]{\;\; #1} % Star symbol used as prefix in front of a paragraph with no indent \newcommand{\prefstar}{\noindent$\ast$ } % Big vertical line restricting the function. % Example: $u(x)\restrict_{\Omega_0}$ \newcommand{\restrict}{\big\vert} % Math operators which are typeset in Roman font \DeclareMathOperator{\sgn}{sgn} % Sign function \DeclareMathOperator{\erf}{erf} % Error function \DeclareMathOperator{\Bd}{Bd} % Boundary of a set, used in topology \DeclareMathOperator{\Int}{Int} % Interior of a set, used in topology \DeclareMathOperator{\rank}{rank} % Rank of a matrix \DeclareMathOperator{\divergence}{div} % Curl \DeclareMathOperator{\curl}{curl} % Curl \DeclareMathOperator{\grad}{grad} % Gradient \DeclareMathOperator{\tr}{tr} % Trace \DeclareMathOperator{\span}{span} % Span $$

止于至善

As regards numerical analysis and mathematical electromagnetism

摘要: This post summarizes the proof for Theorem 7.9 in Royden's "Real Analysis". Theorem 9 If $\langle X, \rho \rangle$ is an incomplete metric space, it i 阅读全文
posted @ 2020-09-26 17:39 皮波迪博士 阅读(220) 评论(0) 推荐(0) 编辑