Day: June 4, 2020

topological lists

(suggested new terminology)
We often need to take into account relatedness, and the mathematical discipline of ‘General Topology’ (simply ‘topology’ for short, herein) is the rigorous characterization of relatedness. The mathematical discipline considers every shade and nuance of relatedness, but in practical matters of immediate concern it is convenient to confine our attention to two types of relatedness: ‘strong’ and ‘weak’, with the default being ‘strong’. To illustrate, let us consider food. What is related to food? There is no question that salt, for example, while not a food, is related to food. This is an example of ‘strong’ relatedness. What about beverages? Here there is a choice of relatedness. We may or may not, in a given circumstance, wish to consider beverages as being ‘related’ to food. So, if we choose to consider beverages to be related to food, this would be an example of ‘weak’ relatedness. So, an expression of the form ‘a topological list of X’ is to be understood as being short for ‘a list of items of X, together with items that are strongly related to X’. To take the case of food, ‘a topological list of food’ means ‘a list of items of food, together with items that are strongly related to food’. In particular, to exploit the mathematical terminology further, we can say that salt, for example, is in the (topological) boundary of food. We can also say that salt, for example, is in the (topological) closure of food.
Note that this is not the first time that topology has been applied to the nitty-gritty of the real world: Kurt Lewin, the founder of Social Psychology, did so in his book ‘Principles of Topological Psychology’.
keywords:
[Mathematics]
[topological boundary of a set]
[topological closure of a set]