# Questions tagged [gn.general-topology]

Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

2,970 questions
149 views

### Rays in non-compact spaces

According to the book Infinite homotopy theory by Baues-Quintero, if $X$ is a locally compact, locally connected, connected metrizable space, its Freudenthal ends can be identified (Proposition 9.20) ...
134 views

### Are there any non-trivial convergent sequences in the maximal ideal space of the measure algebra?

Consider the measures on the circle, $M(\mathbb T)$, endowed with the convolution product which makes it a unital Banach algebra under the total variation norm. Denote by $\Delta$ the maximal ideal ...
189 views

### Doubling dimension vs other metric dimensions

For separable metric spaces, three fundamental notions of dimension are equivalent: $$\text{dim }X = \text{Ind }X = \text{ind }X ,$$ Where does the doubling dimension fit into the picture?
123 views

### Trees and Shabat polynomials

Recently, I read the relation between Shabat polynomials and trees. The book [0] says that if $p: \mathbb{C} \to \mathbb{C}$ is a degree-$n$ polynomial such that the segment $[-1,1]$ contains no ...
209 views

189 views

61 views

394 views

94 views

### The first homotopic Baire class

Let $X$ and $Y$ be topological spaces. A map $f:X\to Y$ belongs to the first Baire class (to the first homotopic Baire class), if there exists a continuous map $H:X\times \omega\to Y$ (a continuous ...
364 views

### Does the lattice of all topologies embed into the lattice of $T_1$-topologies?

Let $\kappa$ be an infinite cardinal, and let $\text{Top}(\kappa)$ be the lattice of all topologies on $\kappa$, ordered by $\subseteq$. Let $\text{Top}^{T_1}(\kappa)$ be the lattice of all $T_1$-...
76 views

### Union of Two Faces, using the Jordan Curve Theorem

Consider four disjoint points in the plane, $v_{1}$, $v_{2}$, $v_{3}$ and $v_{4}$. The cycle, $C:=v_1v_2v_{3}v_{4}v_{1}$, is the union of the (Jordan) arcs, $A_{12}$, $A_{23}$, $A_{34}$, and $A_{41}$, ...
83 views

### Connected $T_2$-space such that not all closed subsets are fibers

If $(X,\tau)$ is a topological space, then we say $A\subseteq X$ is a fiber if there is $f:X\to X$ continuous and $y\in X$ such that $A = f^{-1}(\{y\})$. For any $T_1$-space it is clear that fibers ...
196 views

### Is there a compactification with nontrivial connected remainder?

Question: Let $X$ be a continuum and $p \in X$. Under what conditions does there exist a compactification $\gamma (X-p)$ with $\gamma (X-p) - (X-p)$ connected and nondegenerate? Throughout, $X$ is a ...
237 views