The Wikipedia entry 'Topology' describes topology as 'topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.'. But I'm not sure if that sentence correctly describes what topology is, I think it just describes a part of topology or some applications of topology. Nevertheless I think the Wikipedia article about topological space does better in explaining the generality of the concept, and also the main idea about topology (which is generalising the notion of space, in my opinion). Do you agree with me? Shall we change that Wikipedia entry and make it closer to the 'Topological space' one?
By the way, I'm sorry if this question turns out to be not appropriate for this forum.
Edit: I mean, isn't topology more than 'deformation of geometric objects'? Some topologies can be finite or just not related to the Euclidean spaces, how can we talk about 'deformation of geometric objects' in those topologies? or even about 'stretching, twisting, crumpling and bending'?
In the category $\mathsf{Top}$ of topological spaces the morphisms are precisely the continuous maps and the isomorphisms are homeomorphisms.
In other words, two homeomorphic spaces are, in the category $\mathsf{Top}$, up to isomorphism, considered to be indistinguishable.
Now homeomorphic spaces are in particular homotopy equivalent. And the notion of homotopy equivalence provides the intuitive picture of two spaces that are being continuously stretched and deformed into one another.
That's why we often talk about continuous deformations whenever the question arises what Topology in layman's terms actually is about.
Note that the Wikipedia article also refers to the Wikipedia articles about general topology, geometric topology, differential topology and algebraic topology.
In my opinion, the introduction on the main article about Topology on Wikipedia is fine.