TITLE: How to avoid getting "lost in notation"
QUESTION [9 upvotes]: Having just finished my first (and wonderful) year of undergraduate math studies, there is a certain "skill" I find myself still struggling with, as if I've made no progress regarding it since my first lecture in my first course.
As the title subjects, I'm referring to being able to keep track of the different notations, scripts, symbols assigned "on the fly" to note specific objects, either during lecture, or when I find mydelf reading a mathematical text.
It's important to emphasize that I'm not referring to the difficulty of understanding formal / rigorous proofs, but simply to that of keeping track of all the different objects currently under discussion.
I'll provide two examples to illustrate what I mean more concretely:

This is a direct construction of a completion for some metric space. I find myself easily getting lost between all of the possible combinations of ($[x] \ \hat{x} \ x \ x_n \ \langle x \rangle $), even though these notations are used to refer to completely different things. This confusion persists even after I know the proof good enough to write it down and explain it myself.
This simple exercise, that involves showing that if a locally compact subset $A$ of some topological $T_2$ space $X$, is dense ($A$ is dense in $X$), than $A$ is open. Even though after finishing my topology course, the exercise itself seems easy, I find it overwhelmingly hard to read the short answers in the link provided. The hardest part: remembering what $V, U, O, D, A, X$ all stand for, and transitioning every single moment form treating (for example) U as a subset of spaces, $D$, or $A$, or $X$.

Now the main frustration is that I can easily find myself investing a great deal of time when reading material. Alternatively, during lecture I can find myself totally lost.

Question:
What can one do improve his ability to quickly "digest" patterns, notation, values, etc. (In other words - to avoid the difficulty I've just described)?
  I would especially appreciate those who've had the same struggles and found a way to deal with it.

A couple of remarks:

I know that a lot (maybe most) of people seem to be completely unaffected by this kind of difficulty, but I'm also pretty certain that a lot of students are familiar with this problem. Thus - I find it relevant to post as question on this site.
I've found the following question relevant, but not the same: This one explicitly states similar challenges (among other things) regarding notation, but answers seem to focus on how mathematicians write in order to make their ideas easier to read.

REPLY [2 votes]: Like anything else, practice. It's important tho not to get discouraged. You have to accept this is part of the process of learning anything new, and when you find yourself in that place were your head hurts, don't run from it, because that is where you want to be. That is where learning takes place. Instead of wasting 15 free minutes on facebook, browse some problems on here. Just try and make sense of what the problem is asking, make your brain hurt, but make it hurt on things you can figure out.
It's also really helpful to bookmark some problems that you struggled with at one point, so you can go back later and see the progress you've made. Just being aware that you have made progress, both feels really good, and helps you to stay positive as you struggle forward.
Also, this isn't unique to you, its something everyone has to go through.
Math truly is a language. Just because it's in english (well most of it, lol) doesn't mean you should be able to instantly understand it. You wouldn't expect yourself to understand Spanish or French or some other foreign language right away, would you? Give yourself that same freedom with math.