\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Topology
Finer and coarser topologies
We say that one topology \( \mathcal{T} \) on \( X \) is
finer than another topology \( \mathcal{T}' \) on \( X \)
iff [in words...].
\( \mathcal{T}' \) is said to be coarser than
\( \mathcal{T} \).
Stronger and weaker are alternative
terminology for finer and coarser.
\( \mathcal{T} \) is strictly finer iff [...]
Symbolically,
- \( \mathcal{T} \) is finer than \( \mathcal{T}' \) ⟺ [...].
- \( \mathcal{T} \) is strictly finer than \( \mathcal{T}' \) ⟺ [...].
