simply connected

In this example, the surface is not simply connected and any smoothed-out object looks like a torus with at least one hole.

Any object with a simply connected surface can be smoothed out to look like a sphere.

In this example, mathematicians would say that the surface of the apple is "simply connected" .

Just push it a little bit. So, in fact, this is simply connected. That was a trick question.

Spacetime also appears to have a simply connected topology, at least on the length-scale of the observable universe.

Let's not worry too much about it. For accuracy we need our vector field to be defined in a simply connected region.

OK, so that's the definition of the surface of a sphere being simply connected.

OK, so space with the origin removed, OK, you think it's simply connected?

Finally, we classify the twisted conjugate actions of simply connected complex simple Lie groups associated with complex automorphisms.

So, that's one way to check just for sure that this thing is not simply connected.

OK, so for this guy, domain of definition, which is plane minus the origin with the origin removed is not simply connected.

And, that's where the assumption of simply connected is useful.

OK, so where do we use the assumption of being defined in a simply connected region?

In many ways, I simply connected the dots in these different strands of thinking and warnings.

As mathematicians say, "Every simply connected closed 3-manifold is homeomorphic to a 3-sphere. "

OK, so anyway, that's the customary warning about simply connected things.

Or, as we will see soon, in a simply connected region.

S OK, so we can find S, a surface, S, that bounds C because the region is simply connected.

Analytically Modeling of Complicated Boundary Simply-connected Region Conformal Mapping

Non-simply Connected Compact Manifold with Nonnegative Curvature

P-Harmonic maps for simply connected manifolds with nonpositive curvature

Inverse Mode Problems for Simply Connected Spring-Mass Systems