Topological Spaces-Homeomorphisms
المؤلف:
David R. Wilkins
المصدر:
Algebraic Topology
الجزء والصفحة:
8
26-9-2016
1798
Definition: Let X and Y be topological spaces. A function h: X → Y is said to be a homeomorphism if and only if the following conditions are satisfied:
• the function h: X → Y is both injective and surjective (so that the function h: X → Y has a well-defined inverse h−1: Y → X),
• the function h: X → Y and its inverse h−1: Y → X are both continuous.
Two topological spaces X and Y are said to be homeomorphic if there exists a homeomorphism h: X → Y from X to Y .
If h: X → Y is a homeomorphism between topological spaces X and Y then h induces a one-to-one correspondence between the open sets of X and the open sets of Y . Thus the topological spaces X and Y can be regarded as being identical as topological spaces.
الاكثر قراءة في التبلوجيا
اخر الاخبار
اخبار العتبة العباسية المقدسة
