I'm a Psychologist and Neuroscientist with interest in math and I just started reading about Topology. I have to say it's not easy to grasp the concepts without a practical example, so I'm trying to understand topology in a practical (psychologically applicable) way.
I was thinking for example about the concept of something being inside of another thing, like someone being inside a house, tea being inside a cup or a smaller circle lying inside a bigger one asf. Humans can identify those things as being the same (belonging to one equivalence class?), i.e. if I ask someone to identify the object inside the other one, every normal functioning person will be able to identify the object inside, no matter how different the properties (color, size, form asf.) of the objects are. So there must be some general properties the brain uses.
But how can I define this concept of being inside another thing topologically/mathematically so that it is applicable for a wide range of objects?
And what if it gets even more complex. What if a time factor is included like putting something inside another thing. For example putting a key inside a keyhole, putting a steak in the frying pan, putting food into a shopping bag asf. So here it's about a processes over time which should belong to the same equivalence class.
How can this be defined?
I hope it became clear what I mean and I'm looking for some inspirational thoughts. Also if anyone can recommend literature with emphasis on practical applications, I'd be thankful :).