In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence. In essence, a sequence is a function with domain the natural numbers, and in the context of topology, the codomain of this function is usually any topological space. However, in the context of topology, sequences do not fully encode all information about a function between topological spaces. In particular, the following two conditions are not equivalent in general for a map f between topological spaces X and Y:
The map f is continuous (in the...
In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.
== Definition ==
A real-valued function
f
{\displaystyle f}
on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any
x
{\displaystyle x}
and
y
{\displaystyle y}
in the interval and for any
α
∈
...
