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.vscode/settings.json
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.vscode/settings.json
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@@ -3,6 +3,10 @@
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{
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"label": "Watch",
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"task": "Watch"
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},
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{
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"label": "Conservative Watch",
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"task": "Conservative"
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}
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],
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"latex.linting.enabled": false,
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.vscode/tasks.json
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.vscode/tasks.json
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@@ -39,6 +39,19 @@
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}
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}
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}
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},
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{
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"label": "Conservative",
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"type": "shell",
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"command": "npx spec watch --conservative",
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"windows": {
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"options": {
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"shell": {
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"executable": "cmd.exe",
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"args": ["/d", "/c"]
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}
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}
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}
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}
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]
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}
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@@ -38,7 +38,7 @@
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\item If $\mathfrak{E}(\sigma, \fU)$ forms a fundamental system of entourages for $\fV$.
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\end{enumerate}
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The uniformity $\fV$ is the \textbf{$\sigma$-uniformity}, and the topology induced by $\fV$ is the \textbf{topology of uniform convergence on the sets $\sigma$}/\textbf{$\sigma$-uniform topology} on $X^T$.
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The uniformity $\fV$ is the \textbf{$\sigma$-uniformity}, and the topology induced by $\fV$ is the \textbf{topology of uniform convergence $\sigma$}, or the \textbf{$\sigma$-uniform topology} on $X^T$.
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\end{definition}
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\begin{proof}
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(1): Since $\Delta \subset E(S, U)$ for all $S \in \sigma$ and $U \in \fU$, $\mathfrak{E}(\sigma, \fU)$ generates a uniformity on $X^T$.
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