When talking about glueing in topology, are you allowed to stretch

File: Mug_and_Torus_morph.gif (497KB, 240x240px) Image search: [Google]

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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.

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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.