Try to do more active stuff. Go for a walk, lift some weights, run around, play a sport. You don't have to be sweating and panting at the end. It is healthy for your brain and mood (particularly with motivation) to stay active.
@SamuelYusim I sympathize with your psychology somewhat. Feeling inferior goes down to a frustrating level sometimes: I stop doing math for days, maybe weeks. Completely understand having more productivity while in home with my family - I was away for like a month or so, about a thousand km away from where my home is, in a relatively well-known university to study math. I didn't feel more productive, although I probably did learn more. I didn't enjoy my time there either.
Though I have realized it's more about being around my home than being together with my family or family doing stuff I feel lazy for. The familiar environment's the issue.
@SamuelYusim I don't know an easy way to prove this. There is a "theorem" that any space of topological dimension $n$ embeds in $\Bbb{R}^{2n+1}$, but I don't know how to prove this.
I heard it from Mike. Maybe you'd find references if you google.
Simplicial complexes are nice enough to have top. dim. n.
A space $X$ is a D-space if whenever one is given a neighborhood $N(x)$ of $x$ for each $x \in X$, then there is a closed discrete subset $D$ of $X$ such that $\{N(x) : x \in D\}$ covers $X$.
The D-space problem is, is every Lindelof space D?
See, not so technical.
You might think about why every compact space is D, as an exercise
some of the stuff i do presumably has a symplectic context, at least to the extent that symplectic manifolds = classical phase space as compared with quantum mechanics
