# Tagged Questions

Questions about algebraic methods and invariants to study and classify topological spaces: homotopy groups, (co)-homology groups, and beyond.

14 views

23 views

### Euler characteristic of closed surface

Assume that you have a closed surface that can be covered by finitely many triangles. Then $K(p)= 6-val(P)$ where P is a vertex and $val(P)$ the number of edges that lead to this vertex. Now, I am ...
24 views

### Cones over a topological space and homotopy!

Let $X$ be a topological space and let $CX$ be the cone over $X$. We identify $X$ with the subspace $X\times \{0\}$ of the cone through the immersion $x \mapsto [(x,0)]$ for $x \in X$. Let $f:X \to Y$ ...
18 views

### smash product does not preserve equivalences: non-example

If $f : X \rightarrow Y$ is a weak equivalence of pointed spaces and $Z$ is a pointed space, then $f\wedge Z : X\wedge Z \rightarrow Y\wedge Z$ is not necessarily a weak equivalence, unless we're ...
17 views

### Fundamental Confusion Regarding the Fundamental Group

Consider the following question. Let $X$ be a topological space and $x_0$ be any point in $X$. Let $\gamma\in \pi_1(X,x_0)$ be a non-constant loop about the base point $x_0$. Then can it happen ...
26 views

15 views

### Liftings of Nullhomotopic Maps

Is the lifting of a nullhomotopic map always a loop in a path connected space? This question is perhaps very trivial,but I am struggling with it. Please help.
21 views

### quotient topology in compact hausdorff space

Let X is compact hausdorff space and A is a subset of X. Show that X/A is Hausdorff ,when A is closed. I have no idea how to proof it. Can you give me a clue?