Productive Property
المؤلف:
Joshi, K. D.
المصدر:
"Productive Properties." §8.3 in Introduction to General Topology. New Delhi, India: Wiley,
الجزء والصفحة:
...
8-8-2021
1956
Productive Property
A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness, and path-connectedness, axioms 
, 
, 
and 
, regularity and complete regularity, the property of being a Tychonoff space, but not axiom 
and normality, which does not even pass, in general, from a space 
to 
. Metrizability is not productive, but is preserved by products of at most 
spaces. Separability is not productive, but is preserved by products of at most 
spaces.
Compactness is productive by the Tychonoff theorem.
REFERENCES:
Joshi, K. D. "Productive Properties." §8.3 in Introduction to General Topology. New Delhi, India: Wiley, pp. 203-209, 1983.
Kelley, J. L. General Topology. New York: Van Nostrand, p. 133, 1955.
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