Subject: Can a structure be built which is tens or even hundreds of miles high?

What are the defined limits of height - of a structure on the earth's 
surface, man-made or natural?. Why, in principle, will it NOT be possible 
for us to construct buildings of ANY given height? Ignoring for the moment 
practical issues of use of such a building, how lifts will work and 
suchlike, can a stable structure of tens or hundreds of miles in height be 
constructed even in theory? It wouldn't matter to me what the ultimate 
appearance of this building was, i.e. whether it had the familiar needle-
like profile of a city skyscraper or resembled a huge artificial mountain; 
I'd just like to know whether it can, in principle, be done. And if so, 
could this building then be used to allow us to access outer space? I have 
this mental image of a spidery network of metal girders, starting out 
really broad at ground level and tapering up towards the summit - 
something resembling the Eiffel tower except on a much, much bigger scale. 
Irrespective of the answer to that question, assuming it COULD be done, 
and that we had somehow constructed a building say 200 miles high, would 
we still need a rocket to provide us with sufficient acceleration to 
escape the earth's gravity?
Much appreciated

Re: Can a structure be built which is tens or even hundreds of miles high?