Recent content by kade

It really upsets me. So if I want to get into this field, I have to apply for another phd after this one is done?

Yea, it looks pretty wield and torturing me, but it does happen. My experience is circuitous. I choose it 'cause I have no other options.

As a fresh pure math phd student, I aim to become a mathematical physicist, and currently I try to schedule out what I should do step by step in this four years on phd program. But in my university, there is no professor in this field could help me as my advisor. So I wish to get some advice...

This example makes sense. I got the picture now. Thank you.

Yea, the inverse image should be connected. But, according to the property of reserving closeness, I am thinking why not define the continuous function as this way: It maps connected subsets in X onto connected subsets in Y; For any connected subset in Y, its inverse image in X is connected.

But I think the continuous function doesn't have to be a bijection. So why should it, the inverse image of open set in Y, be open in X? Why not closed? Or anything else but disjointed.

But, why its reverse image should be open in X? Yep, I got it!

Yeah!

Quoted from Wikipedia, A function between two topological spaces X and Y is continuous if for every open set V ⊆ Y, the inverse image is an open subset of X. How to comprehend this definition in a intuitive way?

I am new here, hope to enjoy the discussion with you