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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.

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Velocity gradient in polar coordinate

I just want to convert velocity gradient in polar coordinate to velocity gradient in Cartesian one (i.e. $\frac{\partial u_r}{\partial r}=f\left(\frac{\partial v}{\partial y}\right)$). How can I ...
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Finite Unions of Dendrites

I will ask the main question first, and then give the motivation for this one! The question is a bit specific, but seems to be the most general question to ask after handling some obvious ...
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Arcs Contained In Continuous Injections of $[0,1)$

Suppose we have a metric space $X$ and a continuous injection from $[0,1)$ onto $X$. The case I had in mind will satisfy that $X$ is compact, but the problem I have can be stated more generally, as ...
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Pathological Continua which are Path Connected and Locally Path Connected.

I'm doing research in generalised inverse limits, and I'm trying to prove a result about circle-like plane continua. Definitions A continuum is a compact, connected metric space. A plane 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 ...
Continuum = compact connected set. Suppose that $U$ and $V$ are nonempty disjoint open subsets of $[0,1]^2$. Is there necessarily a continuum $K\subseteq [0,1]^2$ that divides $U$ and $V$? More ...