History for AnotherPlayArea

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Here is a place to play with diagrams or other tex experiments.
If you want to make your own play page, simply edit this page, and add a link below:
EasyProofOfTychonoff
PropabilityTestPage
BlaBla
For instance HigherHomotopyPlayArea is a link. If there is only a question mark,
then the page has not yet been created. Click on the question mark to create the page.
Have fun, but play nice. This is a great way to learn basic latex interactively.
I tried to include some basic examples below. -"mowsey":http://mowsey.org/
-- 
Here are some more mundane examples:
\begin{enumerate}
\item $2+2=4$
\item $1+2\leq 4$
\item Solve $z^5 = 1$ for $z$. Give at least 2 solutions.
\end{enumerate}
Here are some inline examples. A subset $G$ of a metric space $X$ is open if and only if given any point $g \in G$ there is an $\epsilon > 0$ such that whenever $x \in X$ satisfies $\delta(g,x) < \epsilon$ one must have that $x \in G$. That
is, $G$ is open if and only if every point is interior to $G$. Points are never restricted in their movement to and fro (for small distances), so such a set has a spacious or open feel to it.
If $(X,d)$ is a compact metric space, $(Y, d)$ is a metric space, and $f$ is a continuous map from $X$ into $Y$, then $f(X)$ is compact in $Y$.
Ye olde piecewise function $f(x) = \begin {cases} 1 & \text{ if } x \geq 0 \\ 0 & \text{ if } x<0 \end {cases}$
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This is an alternative universal diagram problem for a fibration.
$ \xymatrix{
E^I \ar@/^1pc/[drr]^{e_0} \ar@/_1pc/[ddr]_{\bar{p}} \ar@/_/[dr]_{d}  \\
&N \ar[r]^{\pi_1} \ar[d]^{\pi_2} \ar@/_/@{..>}[ul]_{s} & E \ar[d]^{p} \\
&B^I \ar[r]^{e_0} & B \\
} $
An $R$-module $E$ is injective if the top diagram can always be
completed.  An $R$-module $P$ is projective if the bottom diagram
can always be completed. All rows are assumed exact.
$ \xymatrix{ 0 \ar[r] & M \ar[r] \ar[d] & N \ar@{-->}[dl] & &   & E\\
                      & E       &&&  N \ar@{-->}[ur] & M \ar[u] \ar[l] & 0 \ar[l] \\
\\
  0 & M \ar[l] & N \ar[l]      & &          & P \ar@{-->}[dl] \ar[d] \\
               & P \ar[u] \ar@{-->}[ur] & & & N \ar[r] & M \ar[r] & 0  } $
TorChase and TorChaseTwo are examples of just pasting some LaTeX on in here.