link between topological and metric spaces

Given a topological space ( X, t ), can we find a metric d s.t. ( X, d
) is a metric space and the topology induced by this metric space is:

1) a subset of
2) exactly equal to
3) a superset of

( X, t )? If yes, how, if not why not?

If someone can point me to an appropriate book or research paper or
give me some pointers about how to solve this, I will be much grateful.

.

Relevant Pages

  • Re: Most powerful IRC client for Unix
    ... functionality is a superset of it. ... Other possibilities are xchat and ... irssi. ... Prev by Date: ...
    (comp.unix.questions)
  • Re: XP Media Edition
    ... It is a superset of XP ... Ken Blake - Microsoft MVP Windows: Shell/User ... Please reply to the newsgroup ... Prev by Date: ...
    (microsoft.public.windowsxp.basics)
  • Re: Forth200x: Serious design flaw in deferred words proposal.
    ... Whether or not they are code pointers has nothing to do with anything. ... fully pregnant as distinct from being partially pregnant. ... whether it is the superset or the subset of the ... capabilities is neither here nor there ... ...
    (comp.lang.forth)
  • Re: Latitude D600 - S-VHS Question
    ... >connector on my TV has 4 pins. ... It's a superset of the 4-pin, the 4-pin plugs right in! ... Prev by Date: ...
    (alt.sys.pc-clone.dell)
  • Universal Definition of Subset
    ... According to the universal definition, does the term "subset" alone ... imply that the subset of a superset may contain 0 elements, ... Prev by Date: ...
    (sci.math)