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--- math104-f21:hw7 [2021/10/15 23:00]
pzhou
+++ math104-f21:hw7 [2022/01/11 08:36] (current)
pzhou ↷ Page moved from math104:hw7 to math104-f21:hw7
@@ Line 50: / Line 50: @@
 We know
-$$ \overline{E^c} = \bigcap \{ K \mid  K \In X \text{is closed}, E^c \In K \} = \bigcap \{ K \mid K \In X \text{is closed}, K^c \In E \} = \bigcap \{ K \mid K^c \In X \text{is open}, K^c \In E \} $$
+$$ \overline{E^c} = \bigcap \{ K \mid  K \In X \text{ is closed}, E^c \In K \} = \bigcap \{ K \mid K \In X \text{ is closed}, K^c \In E \} = \bigcap \{ K \mid K^c \In X \text{ is open}, K^c \In E \} $$
 and
-$$ E^o = \bigcup \{ F \mid  F \In X \text{is open}, F \In E \} $$
+$$ E^o = \bigcup \{ F \mid  F \In X \text{ is open}, F \In E \} $$
 Hence
-$$ (E^o)^c = \bigcap \{ F^c \mid  F \In X \text{is open}, F \In E \} = \bigcap \{ K \mid K^c \In X \text{is open}, K^c \In E \} = \overline{E^c} $$
+$$ (E^o)^c = \bigcap \{ F^c \mid  F \In X \text{ is open}, F \In E \} = \bigcap \{ K \mid K^c \In X \text{ is open}, K^c \In E \} = \overline{E^c} $$
@@ Line 61: / Line 61: @@
 Optional. Let $(X, d)$ be a metric space, $k \geq 1$ be an integer. Let $Conf_k(X) = \{ S \In X, |S|=k\}$, i.e., an element in $Conf_k(X)$ is subset  $S \In X$ consisting of $k$ points. For example, let $X = \R$, $k=2$, then $S = \{ 2, -1.1 \}$ is an element in $Conf_2(X)$. Can you put a metric on $Conf_k(X)$ using $d$?
+See [[https://en.wikipedia.org/wiki/Hausdorff_distance | Hausdorff distance ]]

Lecture Notes