Prove [0,2] is not homeomorphic to the subspace [0,1] U [2,3] of R (usual topology). Proof (from text I'm reading): Let (A,T1) = [0,2], (B,T2) = [0,1] U [2,3] ...
... The existence of f lets us conclude that A is not connected, which is false. So f cannot exist. -- An amateur practices until he gets it right, A...
I thought this would be more difficult since they said "it can be solved with some thought", so I thought it might be challening. In the future I will tag any...
An interesting article that just happens to fit right in with the discussion I've been having with ropestretcher. Its by Keith Devlin, a writer for the...
... upon ... the fact ... [0,1] is ... I came up with an alternative version of this that. So that brings up to three the number of attacks on this proof :)...
Hello. For anyone not into topology, a metric on a space can be thought of as simply a way to measure distances between points in the space. Take the plane...
Hello everybody, Here is a question (asked by a student of mine) which led me to conclude that I'm missing something about the relationship between the...
Russian may have solved great math mystery A publicity-shy Russian researcher who labors in near-seclusion may have solved one of mathematics' oldest and most...
... Since the rationals are dense in the reals, and r1<r2, we can find a rational number between these two reals. Thus, to separate any two real powers, we...
Note, all the information on integrals presented here I got from my old engineering calc book : Calculus with Analytic Geometry 4th edition by Edwards and...
Am I missing something? Begin with background: Theorem: A sequence converges if and only if it is bounded and has exactly one subsequential limit point. ...
You certainly have a lot of off-topic commentary. Please see my ... has ... infinity. If ... finite ... of terms ... contains the entire sequence and all...
... From: klstern3 To: comp-sci-theory@yahoogroups.com Sent: Monday, January 12, 2004 8:22 PM Subject: [comp-sci-theory] Re: Analysis of the reals You...
... and ... a ... number ... original ... contains all but a finite (0) number of elements of itself. I assumed you wanted to show that any subsequence...
Anyways. Another reason why the subsequence version of the theorem may be useful is to prove a sequence does NOT converge. ie: if any subsequence diverges...
Yes, but I guess this is my permeating thought: If you know enough to know that the supremum of the set of subsequential limit points is not equal to the...
hi thank if anybody can help me to prove this problem. It's due on tomorrow. problem: prove that the class of co-r.e. languages is separable. we say that a...
Hi Homi, ... This question sounds familiar...I wonder if it's been discussed here before. You might want to check the archives to see if this problem or...
... From: Kurt Van Etten To: comp-sci-theory@yahoogroups.com Sent: Thursday, January 15, 2004 12:05 AM Subject: [comp-sci-theory] Re: prove that the class of...
... From: Kevin L Stern To: comp-sci-theory@yahoogroups.com Sent: Monday, January 12, 2004 10:54 PM Subject: Re: [comp-sci-theory] Re: Analysis of the reals ...
The SCO Group Inc. finally provided IBM with a list of files and individual code samples that it claims violate its intellectual property rights. In March,...
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