# The weight of H(X) does not exceed the weight of X?

• October 13th 2011, 10:59 AM
student2011
The weight of H(X) does not exceed the weight of X?
Hello;

If $X$ is a space and $H(X)$ denotes the group of homeomorphisms of X with composite between functions as a binary operation. My question is:

Show that the weight of $H(x)$ does not exceed the weight of $X$.

I found the proof in the attached file. But the problem is I could not understand it. So kindly read it and explain to me or if you have any other idea please help me.

The weight of a spaces $W(X)$ is the smallest cardinality of a base of $X$. The Lindelof number $L(x)$ is the least infinite cardinal number http://eom.springer.de/c/images/c020.../c02036011.png such that every open covering of $X$ has a subcovering of cardinality http://eom.springer.de/c/images/c020.../c02036013.png.