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The sheet of paper represents a plane in the spacetime continuum, and the two points represent a distance to be traveled, but theoretically, a wormhole could connect these two points by folding that plane (i.e. the paper) so the points are touching. In this way, it would be much easier to traverse the distance since the two points are now ...
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A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical ...
A space homeomorphic to a subcontinuum of the Euclidean plane R 2 is called a planar continuum. A continuum X is homogeneous if for every two points x and y in X, there exists a homeomorphism h: X → X such that h(x) = y. A Peano continuum is a continuum that is locally connected at each point.
Most well-known space-filling curves are constructed iteratively as the limit of a sequence of piecewise linear continuous curves, each one more closely approximating the space-filling limit. Peano's ground-breaking article contained no illustrations of his construction, which is defined in terms of ternary expansions and a mirroring operator .
The Alaska Airlines pilot who guided 171 passengers and four flight attendants to safety when a door panel blew out of the aircraft wasn’t aware of the mid-flight emergency — but knew ...
Closed graph theorem [5] — If : is a map from a topological space into a Hausdorff space, then the graph of is closed if : is continuous. The converse is true when Y {\displaystyle Y} is compact .