Yes.

Any one body without a handle is topologically the same. Pic related is the Wikipedia pic for one body with one handle (demonstrating homotopy transformations)

related
https://en.wikipedia.org/wiki/Genus_%28mathematics%29#Topology

>>7653054
It sounds like you have a problem visualising the gluing process. Just see what happens as you pull the sides into the two corners while keeping the boundary connected. I think wikipedia has a gif of the process of making a disk into a sphere, probably on the quotient space page.

topology is the shit tho

You are always allowed to stretch in topology -- this is what homeomorphisms buy you. Two spaces are considered to be the same if we can stretch one into another nicely, i.e. without ripping or tearing it.

The bottom quotient space pictured is a nasty thing known as the dunce cap. All I know about the top one though is that Seifert van Kampen gives its fundamental group is Z_3. Anyone know what the literature calls it?

>>7653054
>topography
I took abstract 1&2, Lin 1&2, analysis 1&2, but never had a damn good reason to take topology. It seems 2abstract4me

Like, wtf breh

>>7653093
>>7653208
>>7653475
Alright, thanks. I can visualise it without too much trouble but I only started this course this week and was not entirely sure if this was the way to do it.

>>7653576
See
>>7653472
Thats a good enough reason for me.

>>7653565
I have no idea, but Im going to look into this now.

>>7654609
>>7653576
Undergrad (point-set) topology was kind of boring. It seemed like all these arbitrary rules, until I took grad level analysis. Then it became more interesting.
Algebraic topology is the fucking tits though.

>>7655278
What does grad level (real?) analysis envelope in your uni?

>>7653054
Yep. Topology concerns itself only with connections - the actual shape and scale are irrelevant. Being able to stretch and warp objects as much as you want, as long as you don't change the connectivity, is a generic characteristic of topological anything.>>7653093

Is there a good textbook on topology for scientists and engineers?

Something like Farlow's PDE book. Just an intro into the resulting methods and basic understanding without the rigour and proof autism.