CW-complex, Hausdorff space, second-countable space, sober space
connected space, locally connected space, contractible space, locally contractible space
hom-set, hom-object, internal hom, exponential object, derived hom-space
loop space object, free loop space object, derived loop space
The Whitney $C^k$ topology is a topology on the set $C^\infty(X,Y)$ of smooth functions between two smooth manifolds, induced from the natural topology of the order-$k$ jet spaces of maps from $X$ to $Y$.
Often, and espcially for $k = \infty$ this is just called the $C^k$-topology .
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