- E33
[0HR] Prerequisites:[0KX],[0KZ].Let
, letβs consider the family of parts of comprised ofthe open intervals
with and ,the sets
with and .
Show that
satisfies the properties (a),(b) seen in [0KX]. Let therefore be the topology generated by this base. The topological space is called one-point compactified line. This topological space is and it is compact (Exer. [0JD]); it is homeomorphic to the circle (Exer. [0YF]); therefore it can be equipped with a distance that generates the topology described above.
EDB β 0HR
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English
Authors:
"Mennucci , Andrea C. G."
.
Bibliography
Book index
Book index
- space, topological
- topological space
- base, (topology)
- one-point compactified line
- real line, one-point compactified ---
- real line , see also real numbers
- real numbers , see also real line
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