# Tagged Questions

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### Description of real projective spaces in various contexts

What I want to know is : What is the description of real projective spaces (specially $RP^0$, $RP^1$, $RP^2$) respectively in context of topology, geometry and algebra? I'm searching for simple ...
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### smash product of Eilenberg-Maclane spaces

Let $G$ be an abelian group and $K_n=K(G,n)$ be the Eilenberg-Maclane space. How to obtain $K_m\wedge K_n$ is $(m+n-1)$-connected? (Hatcher's book page 404)
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### homotopy between two functions

Let us discuss this problem: Let $A=\{a_{1},a_{2},\ldots,a_{n}\}$, $B=\{b_{1},b_{2},\ldots,b_{n}\}$ and $C=\{c_{1},c_{2},\ldots,c_{n-1}\}$ be discrete finite sets embedded in a unit sphere ...
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### whether gluing the all faces of finite tetrahedrons in pairs would yield a manifold?

In fact ,I have asked this question in this web.But after read the book recommended to me ,I found this question still can't be solvedã€‚ According to the Theorem 10.1.1 ,Theorem 10.1.2 and the ...
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### genus of a Mobius strip.

So I understand that one can create a closed loop (inside/on) a mobius strip. And cutting if we cut along the loop what remains will still be a connected surface. Meaning that the genus is $\geq 1$. ...
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### A diagram which is not the torus

At page 17 of Munkres' Elements of Algebraic topology it says, referring to fig. 3.6, that "the diagram does not determine [the torus]. It does more than paste opposite edges together": Is it so? I ...
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### finding a topological group with specific conditions

I have a question, it sounds difficult. The question is the following: Let $X$ be a topological group such that the binary operation defined on it is $*$. For any two points $a$ and $b$ in $X$ ...
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### How many triangles are there in each “layer” of Poincaré disk?

Assume we grow from a single triangle layer by layer to get the whole disk. Every time a new ring of triangles makes all the vertices of the triangles already in the picture surround by seven ...