1519 omitted. |
1519 omitted. |
1520 More specifically, $D\to D'$ is an antirefinement if $D'$ is obtained from $D$ by |
1520 More specifically, $D\to D'$ is an antirefinement if $D'$ is obtained from $D$ by |
1521 gluing subintervals together and/or omitting some of the rightmost subintervals. |
1521 gluing subintervals together and/or omitting some of the rightmost subintervals. |
1522 (See Figure \ref{fig:lmar}.) |
1522 (See Figure \ref{fig:lmar}.) |
1523 \begin{figure}[t]$$ |
1523 \begin{figure}[t]$$ |
|
1524 \definecolor{arcolor}{rgb}{.75,.4,.1} |
1524 \begin{tikzpicture} |
1525 \begin{tikzpicture} |
1525 \fill (0,0) circle (.1); |
1526 \fill (0,0) circle (.1); |
1526 \draw (0,0) -- (2,0); |
1527 \draw (0,0) -- (2,0); |
1527 \draw (1,0.1) -- (1,-0.1); |
1528 \draw (1,0.1) -- (1,-0.1); |
1528 |
1529 |
1529 \draw [->,red] (1,0.25) -- (1,0.75); |
1530 \draw [->, arcolor] (1,0.25) -- (1,0.75); |
1530 |
1531 |
1531 \fill (0,1) circle (.1); |
1532 \fill (0,1) circle (.1); |
1532 \draw (0,1) -- (2,1); |
1533 \draw (0,1) -- (2,1); |
1533 \end{tikzpicture} |
1534 \end{tikzpicture} |
1534 \qquad |
1535 \qquad |
1535 \begin{tikzpicture} |
1536 \begin{tikzpicture} |
1536 \fill (0,0) circle (.1); |
1537 \fill (0,0) circle (.1); |
1537 \draw (0,0) -- (2,0); |
1538 \draw (0,0) -- (2,0); |
1538 \draw (1,0.1) -- (1,-0.1); |
1539 \draw (1,0.1) -- (1,-0.1); |
1539 |
1540 |
1540 \draw [->,red] (1,0.25) -- (1,0.75); |
1541 \draw [->, arcolor] (1,0.25) -- (1,0.75); |
1541 |
1542 |
1542 \fill (0,1) circle (.1); |
1543 \fill (0,1) circle (.1); |
1543 \draw (0,1) -- (1,1); |
1544 \draw (0,1) -- (1,1); |
1544 \end{tikzpicture} |
1545 \end{tikzpicture} |
1545 \qquad |
1546 \qquad |
1548 \draw (0,0) -- (3,0); |
1549 \draw (0,0) -- (3,0); |
1549 \foreach \x in {0.5, 1.0, 1.25, 1.5, 2.0, 2.5} { |
1550 \foreach \x in {0.5, 1.0, 1.25, 1.5, 2.0, 2.5} { |
1550 \draw (\x,0.1) -- (\x,-0.1); |
1551 \draw (\x,0.1) -- (\x,-0.1); |
1551 } |
1552 } |
1552 |
1553 |
1553 \draw [->,red] (1,0.25) -- (1,0.75); |
1554 \draw [->, arcolor] (1,0.25) -- (1,0.75); |
1554 |
1555 |
1555 \fill (0,1) circle (.1); |
1556 \fill (0,1) circle (.1); |
1556 \draw (0,1) -- (2,1); |
1557 \draw (0,1) -- (2,1); |
1557 \foreach \x in {1.0, 1.5} { |
1558 \foreach \x in {1.0, 1.5} { |
1558 \draw (\x,1.1) -- (\x,0.9); |
1559 \draw (\x,1.1) -- (\x,0.9); |