Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [continuum-theory]

For questions from continuum theory. A continuum is a compact connected metric space (sometimes this term is used for a compact connected Hausdorff space). Do not use this tag for questions related to the Continuum Hypothesis in Set Theory.

12
votes
2answers
317 views

Equivalence relation on a continuum

Let $X$ be a continuum $=$ a connected compact metric space. Define $x\sim y$ if $x$ and $y$ are contained in a nowhere dense subcontinuum of $X$. It is easy to see that $\sim$ is an equivalence ...
1
vote
0answers
40 views

Trace of diffusion equation matrix

I'm studying waves moving through mediums and I come across this type of equation a lot while describing acoustic waves speed and stress on the material, $$\begin{gather} \frac{\partial}{\partial z}\...
1
vote
1answer
226 views

Prob. 6, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: For a well-ordered set $X$, $X\times[0,1)$ in the dictionary order is a linear continuum [duplicate]

Here is Prob. 6, Sec. 24, in the book Topology by James R. Munkres, 2nd edition: Show that if $X$ is a well-ordered set, then $X \times [0, 1)$ in the dictionary order is a linear continuum. ...