2021/03/01/cohomology-intuitively

[utterances-bot]

Cohomology Intuitively | Chris Grossack's Blog

Chris Grossack's math blog and professional website.

https://grossack.site/2021/03/01/cohomology-intuitively.html

[kikrishn]

Could you please what the intermediate value theorem is in the complex analysis setup?

[kikrishn]

Your blog looks cleaner and has wider latex compatibility? Could you please tell me where to get the format you have?

[HallaSurvivor]

@kikrishn -- We're still using the "ordinary" intermediate value theorem. In fact, I don't know of a complex analogue (besides connectedness, which is a blog post I've considered writing). The idea is to look at the real and imaginary parts of sqrt(z) separately. For instance, re(sqrt(1)) is positive, and is never 0 if we take the short path to i. So re(sqrt(i)) must be positive too. Then moving from i to -1, we look at im(sqrt(i)), which is positive, so we must have im(sqrt(-1)) positive too. Which forces sqrt(-1) = i. We can continue in this way until we find sqrt(1) must actually be -1, which is a problem.

[HallaSurvivor]

As for my format, it was made by Remy Davison. If you contact him, you might be able to commission one as well. It uses jekyll and mathjax on the front end, and I think you can find pre-made jekyll themes if you don't want to pay Remy (or another designer) to make one for you.

[kikrishn]

May I ask you a question in measure theory?

On Fri, 24 Sep 2021, 8:59 am Chris Grossack, @.***> wrote:

As for my format, it was made by Remy Davison https://remydavison.com/development/grossack-site. If you contact him, you might be able to commission one as well. It uses jekyll https://jekyllrb.com/ and mathjax https://www.mathjax.org/ on the front end, and I think you can find pre-made jekyll themes if you don't want to pay Remy (or another designer) to make one for you.

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[HallaSurvivor]

@kikrishn -- it's probably better to ask on mse.

[mmeessiihh]

All you have been kind enough for us is cohomology under set-differential double modalities . I am thinking of a line(fibre)-cohomology modality , Sir . . ..
REZA SANAYE