M 00_03_joinTrees.md +3 -3
@@ 31,17 31,17 @@ Let
$g \colon \big[-3, 3 + \frac{1}{4}\big] \rightarrow \R, x \mapsto 6x$.
The following image shows the graphs of $f$ and $g$.
- \
+ \
The next image shows the corresponding epigraphs.
- \
+ \
And a visualization of their join trees,
i.e. the Reeb graphs of their epigraphs,
is shown in the image below.
- \
+ \
Before we get to interleavings we make some auxiliary definitions.
M 04_RGraphs.md +1 -1
@@ 33,7 33,7 @@ If $X$ is the $\{a_1, a_2, a_3\}$-skelet
in example @constructible-example,
then the following image shows $\mathcal{C} X$.
- \
+ \
Now let $S = \{a_1 < a_2 < \dots < a_n\} \subset \R$ for some
non-negative integer $n$.
M 06_interleavingGraphs.md +1 -1
@@ 34,7 34,7 @@ A picture of $\mathcal{C} X$ is shown in
In the following image we depict the sets $V_{0 3}$ and $V_{0 4}$.
\
+ img/mpl/push-example-delta)\
The left graphic shows the two
connected components of the multigraph with vertices $V_1 \coprod V_2$
M 99_02_constructibleRSpaces.md +1 -1
@@ 46,7 46,7 @@ The following image depicts the geometri
and the associated height function of an
$\{a_1, a_2, a_3\}$-skeleton for an $\overline{\R}$-space.
- \
+ \
Now let $S = \{a_1 < a_2 < \dots < a_n\} \subset \R$ for some
non-negative integer $n$
M 99_03_RGraphs.md +1 -1
@@ 33,7 33,7 @@ If $X$ is the $\{a_1, a_2, a_3\}$-skelet
in example @constructible-example,
then the following image shows $\mathcal{C} X$.
- \
+ \
Now let $S = \{a_1 < a_2 < \dots < a_n\} \subset \R$ for some
non-negative integer $n$.
M 99_04_skeletenEpigraph.md +1 -1
@@ 22,7 22,7 @@ The left graphic in the following pictur
$\{a_1, a_2, a_3\}$-skeleton for a bounded $\R$-space,
by augmenting the sets of vertices and edges with the discrete topology.
- \
+ \
We ignore the colors for now.
The right graphic shows the corresponding epigraph.
A => img/mpl-htaccess +1 -0
@@ 0,0 1,1 @@
+ForceType image/svg+xml