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Math Help - The weight of H(X) does not exceed the weight of X?

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    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 such that every open covering of X has a subcovering of cardinality .

    Please help me and every guidance is highly appreciated.

    Thaaaaaaaaaaank you in advance
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    Last edited by mr fantastic; October 13th 2011 at 01:05 PM.
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