Convex space
Imagine a big, empty room with no corners or edges. It's round, like a ball or a dome. This is called a convex space!
Now, let's say you have two points inside this room. You want to draw a line between them, but there's a catch - the line has to stay inside the room.
No matter where the two points are, you can always draw a straight line between them inside the room. This is because the room is curved in a way that allows any two points to be connected with a straight line that stays inside the room.
This is what makes a convex space special - it's a space that always allows straight lines to be drawn between any two points inside of it.
Now, let's say you have two points inside this room. You want to draw a line between them, but there's a catch - the line has to stay inside the room.
No matter where the two points are, you can always draw a straight line between them inside the room. This is because the room is curved in a way that allows any two points to be connected with a straight line that stays inside the room.
This is what makes a convex space special - it's a space that always allows straight lines to be drawn between any two points inside of it.