Determining which sets are open?

  • Thread starter Thread starter ~Death~
  • Start date Start date
  • Tags Tags
    Sets
~Death~
Messages
45
Reaction score
0
(1/2,1/3),[1/2,1],[0,1/2]

which are open in the subspace topology of the subspace [0,1] of the lower limit topology on R
 
Mathematics news on Phys.org
Use the definition! Which of those is the intersection of [0, 1] with a set open in R (using the lower limit topology, of course)?
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

I (0,1) is uncountable using binary expansions?
Replies
15
Views
2K
I 2-sphere intrinsic definition by gluing disks' boundaries
Replies
8
Views
339
I ##SU(2)## homeomorphic with ##\mathbb S^3##
2
Replies
61
Views
5K
I Is the Projection Restriction to a Linear Subspace a Homeomorphism?
Replies
8
Views
3K
I Fiber bundle homeomorphism with the fiber
Replies
43
Views
5K
I ##SO(3)## topology
Replies
29
Views
3K
I Map possible values of a set with a condition to the naturals
Replies
8
Views
1K
I Is [0,1] under the subspace topology Hausdorff, Compact, or Connected?
Replies
15
Views
2K
B Is the Explanation of Compactness in [0,1] and (0,1) Accurate?
Replies
24
Views
2K
MHB Find Probability of Male Mouse Given Gray: 8 Mice, 3 Males
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top