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A continuum $X$ is called minimal if it is not a single point and is homeomorphic to all its nontrivial subcontinua. Here a trivial continuum is a single point. … What is an example of a minimal continuum not homeomorphic to the interval? This question is motivated by the following post and its related linked questions. Two consecutive continua …

Here, a curve means a homogeneous metric continuum of dimension 1. Can someone explain this definition in different, more elementary, terms, and give some examples to illustrate the meaning? …

Consider the contractible continuum $$A=(Z\times[-1,1]\times\{0\})\cup([-1,1]\times\{0\}\times\{0\})\cup(\{0\}\times\{0\}\times[0,1]),$$ which looks like an antenna. … Give a short and correct proof of the non-planarity of the continuum $A$ (maybe with some references). Thank you. …

Continuum means compact and connected. … Is there a fractal plane continuum which has order $\aleph_0$ at each of its points? …

A continuum is a compact connected metrizable space. … I was recently surprised by the fact that a continuum $X$ can be both arc-like and circle-like, with the example given by Illanes and Nadler in Hyperspaces being the following continuum, obtained by attaching …

Let $X$ be a metric continuum (compact + connected) which is the one-to-one continuous image of the interval $[0,\infty)$. Such an $X$ is called a linear continuum. …

A continuum is a compact connected metrizable topological space. … Is it consistent with $\mathsf{ZFC}$ to have a continuum $X$ with $\aleph_0<\mathrm{disc}(X)<\mathfrak c$? …

Continuum $=$ compact connected metric space. Let $X$ be a continuum. $X$ is indecomposable means that every proper subcontinuum of $X$ is nowhere dense in $X$. … Given the wealth of examples in continuum theory, the answer is likely no. So what is an example of a decomposable continuum all of whose connected open subsets are dense? …

By a metric continuum we understand a connected compact metric space. Let $p$ be a positive real number. … By my answer to the question of Anton Petrunin, each plane continuum is almost $\ell_1$-connected. By analogy it can be shown that each continuum in $\mathbb R^3$ is $\ell_2$-connected. Problem. …

Suppose $C$ is a plane continuum (i.e. a compact, connected set in the plane), contained in the square $S=[-1,1]^2$, but missing the closed vertical line segment $I = \{0\}\times[0,1]$. … : Does there exist a continuum $C$ (contained in $S$, missing $I$, and containing $P(0,-1)$, $Q(-1,1)$, and $R(1,1)$) such that no matter how we pick $z\in[0,1]$ and a subcontinuum $K_z$ containing …

Since there are L-spaces (provably in ZFC), under CH we have regular, hereditarily Lindelöf spaces with density continuum. …

Is each Peano continuum a topological fractal? …

Motivated by Continuum image of line is chainable? A planar continuum $X$ is a compact, connected subset of the plane. …

Continuum means compact connected metrizable with more than one point. A continuum is Suslinean if every collection of pairwise disjoint subcontinua is countable. … In Example 3 at the end of Paper A, there is constructed a continuum $Y:=X/\sim$ which is the quotient of another continuum $X$. …

Kinoshita proved that contractible continuum do not have FPP, but his example is not locally connected. Maybe if we add this to the conditions it will have FPP? P.S. … Continuum as a nonempty compact connected metric space P.S.2. Asked this question here, but smart guy in comments to his answer advise me publish it here …