My first question/confusion is regarding the definition of reduced suspension $\sum X$ and suspension $SX$ of a space $X$. Usually, we denote the quotient space of $X$ with subspace $A$ identified to a point as $X/A$. I understand that suspension of a space is like a 'double-cone': we take a spac...

Context/Background: Often it is asked in some exams - what is the space obtained by collapsing meridional and longitudinal circle of a Mobius strip or similar type of things. When I look at the solutions available, they usually start with a rectangle, then do identifications in an order that is d...

I'm trying to do exercise 5 on page 18 in Hatcher: Show that if a space $X$ deformation retracts to a point $x \in X$, then for each neighborhood $U$ of $x$ in $X$ there exists a neighborhood $V \subset U$ of $x$ such that the inclusion map $V \rightarrow U$ is nullhomotopic. My question: Does...

Show that if a space $X$ is deformation retract to a point $x \in X$, then for each neighbourhood $U$ of $x$ $\exists$ a neighbourhood $V \subset U$ of $x$ s.t the inclusion $V \to U$ is nullhomotopic. Now considering the deformation retract $f: X \times I \to X$ if we just restrict $X$ to $U$ t...

Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able to be tackled by artificial intelligence? Is there some areas of math where some open conjecture...

For any polynomial map $f$ we can define the filled Julia $K$ to be closure of the complement of $ \Omega$ in $\mathbb{C}$ of the basin of infinity $$\Omega = \{z \in \mathbb{C}; f^{\circ n}(z)\rightarrow \infty \}.$$ Thus the boundary of $K$ is what is often called the Julia set. Now there are e...