L-infinity and weak-star topology While reading economics papers, especially those related to economy with land, I often encounter the terms $L^\infty$ and the "weak* topology". They seem like very basic terms, but I couldn't find a basic explanation of them. Here is a typical paragraph which I am trying to decipher (it is from page 4 at the introduction of A foundation of location theory):



Let:

$$[0,\frac{1}{n}]\cup[\frac{2}{n},\frac{3}{n}]\cup[\frac{4}{n},\frac{5}{n}]\cup...\cup[\frac{n-2}{n},\frac{n-1}{n}]$$

$(n=1,2,...)$ represent a sequence of commodities of increasing utility. If the indicator functions of these sets are embedded in $L^\infty$ with the weak* topology, then the limit is $\frac{1}{2}1_{[0,1]}$, half the indicator function on the interval $[0,1]$. This, indeed, is a natural limit that is not in the commodity space.



So my questions are:


What is $L^\infty$?
What is the "weak* topology"?
What is the meaning of "embedded in $L^\infty$"?


NOTE: I have some basic (undergraduate) knowledge of topology. I have heard about "weak topology" but never heard of "weak* topology". I will be very thankful for a simple, intuitive explanation that will help me continue reading!
$L^{\infty}$: the (Banach, usually) space of bounded measurable functions modulo the equality almost everywhere. Like all function spaces not involving holomorphic functions, it's really a space of equivalence classes.

weak-$^*$ topology: the topology on the dual $X^*$ of any topological vector space $X$ induced by the $(X, X^*)$-pairing. 

"embedded in $L^{\infty}$": a (say) topological vector space $Y$ is said to be embedded in $L^{\infty}$ if there is an injective continuous linear map from $Y$ to $L^{\infty}$. 

(This is the usual meaning. In your paragraph, "embedded" just means viewing those indicator functions as representatives of their classes. The weak-$^*$ topology on $L^{\infty}$ is given by the identification $L^{\infty} = (C_0)^*$.)