# Meaning of Space?

1. Jan 22, 2007

### Swapnil

What is the meaning of 'Space' (in the context of vector spaces, Banach spaces, etc)? Is space just another name for a set?

2. Jan 22, 2007

### morphism

It depends on the context... But in general, a space is a set (or class or collection of mathematical objects) with some special properties (e.g. it is equipped with certain operations which in turn satisfy certain requirements). In essense, it's the universe you're going to work in, hence the name.

3. Jan 22, 2007

### Swapnil

So, for example, a Boolean Space $$\mathcal{B}$$ would be a set of two elements 0 and 1 equipped with two binary operations $$\lor$$ and $$\land$$ and an unary operation $$\lnot$$ such that the usual axioms of associativity, commutativity, distributivity, etc hold. Right?

Last edited: Jan 22, 2007
4. Jan 22, 2007

### mathwonk

well it sounds better than banach doo hickey.