\node (j1) at (0,1) {$\color{red}\bullet$};
\node (j0) at (0,0) {$\color{red}\bullet$};

\node (mid) at (0,0.5) {};

\draw[color=red] (j1) -- (j0);

\node (i0j1) at (1,1) {$\color{red}\bullet$};
\node (i0j0) at (1,0) {$\color{red}\bullet$};
\node (i1j1) at (2,1) {$\bullet$};
\node (i1j0) at (2,0) {$\bullet$};

\draw[color=red] (i0j1) -- (i0j0);
\draw (i0j1) -- (i1j1) -- (i1j0) -- (i0j0);

\node (mid2) at (1,0.5) {};

\draw[->] (mid) -> (mid2);

\node (F) at (-0.6, 0.5) {$\mathcal{F}$};
\node[fit=(j0)(i1j1), left delimiter=(, inner sep=-0.7ex, right delimiter=)] (openF) {};

\node (colon) at (2.6, 0.5) {$:$};

\node (F2) at (2.9, 0.5) {$\mathcal{F}$};

\node (fi0j1) at (3.5,1) {$\color{red}\bullet$};
\node (fi0j0) at (3.5,0) {$\color{red}\bullet$};
\node (fi1j1) at (4.5,1) {$\bullet$};
\node (fi1j0) at (4.5,0) {$\bullet$};

\draw[color=red] (fi0j1) -- (fi0j0);
\draw (fi0j1) -- (fi1j1) -- (fi1j0) -- (fi0j0);
\node[fit=(fi0j0)(fi1j1), left delimiter=(, inner sep=-0.7ex, right delimiter=)] (openF2) {};

\node (F3) at (6.1, 0.5) {$\mathcal{F}$};

\draw[->] ([xshift=2.1ex]openF2.east) -- (F3);

\node (fj1) at (6.7,1) {$\color{red}\bullet$};
\node (fj0) at (6.7,0) {$\color{red}\bullet$};
\node[fit=(fj1)(fj0), left delimiter=(, inner sep=-0.7ex, right delimiter=)] (openF3) {};
\draw[color=red] (fj1) -- (fj0);