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A class of transformations of the plane

Published online by Cambridge University Press:  24 October 2008

G. A. Hedlund
G. A. Hedlund
Affiliation:
The Institute of Advanced Study Princeton, New Jersey, U.S.A.
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Extract

Let Z denote the extended complex plane with the natural topology. That is, Z consists of the finite complex plane Zf together with a point, denoted by ∞, any neighbourhood of which consists of the union of this point and the complement of a bounded set of ZF. Let Z* = [z │ z ↦ Z, z ╪ 0, z ╪ ∞]. Thus Z is homoeomorphic to a 2-sphere and Z* is homoeomorphic to a cylinder.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 554 - 564
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

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