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4h
comment Graph connected does not imply $f$ is continuous
Thanks. :) If you add your example to your question I'll vote to re-open, and will undelete my example, which is has a path-connected graph but is continuous at only one point. (With a small modification based on agha's answer, you can arrange a connected graph for a function that's discontinuous everywhere.)
4h
comment Description of $(T\Bbb{CP}^1)^\perp$
@user233339: You're welcome. :) Griffiths and Harris is one possibility, but I recall gleaning a lot of these factlets here and there. (Having an encyclopedic advisor helped.) There are a number of new (published since 2000) books on complex geometry, so there may well be good references I don't know of....
7h
answered Description of $(T\Bbb{CP}^1)^\perp$
9h
answered When are two series the same?
11h
answered A regular surface with non zero mean curvature is orientable
13h
answered Preimage surfaces.
1d
comment projective space and torus
FWIW, a torus can be covered by two annular charts; think of gluing two U-shaped tubes at their ends.
1d
comment Graph connected does not imply $f$ is continuous
Your example seems correct, but the final assertion (a set with connected closure is connected) looks suspicious, e.g., $(-1, 0) \cup (0, 1)$...? (The converse is true: The closure of a connected set is connected.)
1d
comment Graph connected does not imply $f$ is continuous
Any thoughts of your own, or indication of how rigorous an example you're seeking? (Examples suitable for multivariable calculus or for topology may look rather different.)
1d
revised Graph connected does not imply $f$ is continuous
LaTeX-ified
1d
answered Graph connected does not imply $f$ is continuous
1d
comment Implicit Function Theorem Zero
@hartlw: "Implicit differentiation" is a great point. :) Separately, FYI, Math.SE is intended to be a long-term repository for mathematical questions (one per page) and answers. (That is, despite appearances, it's not a mathematical forum/chat site.) In some of your answer posts on this page it appears you've asked new questions. If you have other questions (even if closely related to this one), the preferred action is to ask a a new question. There's more information about the site here and here.
1d
answered determination of the volume of a parallelepiped
1d
comment Finding surface area S using area of projection of S??
@Nancy: Could you please explain what part you didn't understand? Particularly, at what stage of writing out for yourself the provided sketch did you run into obstacles? (E.g., do you know how to compute a cross product? Do you know how to find the magnitude of a vector? Did you compute the four magnitudes, but you aren't able to see how they're related?) Thanks. :)
2d
comment Soft Question: Difficult to Visualize Areas of Mathematics
Regarding flat rectangular tori in $\mathbf{R}^{3}$...it's trivial to roll a paper rectangle into a cylinder, press it flat, then roll the resulting "tubular band" into a cylinder to create a flat torus. Naturally the result isn't immersed, but the flat, toroidal geometry is perfectly apparent. :)
2d
answered Finding surface area S using area of projection of S??
2d
answered Analyzing if function is “onto”
2d
answered Prove that this application $f:S^n\rightarrow \mathbb{RP}^n$ is a local diffeomorphism, alternative approach using curves
2d
answered Monotonous everywhere function
2d
revised Open Unit Ball diffeomorphic to the Open Unit Cube
Changed "sphere" to "ball" in title, and added "open"; one LaTeX tweak.