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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A functional characterization of primitive base


Author: Howard H. Wicke
Journal: Proc. Amer. Math. Soc. 72 (1978), 355-361
MSC: Primary 54E99; Secondary 54A99
DOI: https://doi.org/10.1090/S0002-9939-1978-0507338-6
MathSciNet review: 507338
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Abstract: All published formulations of the concept of primitive base involve the concept of well ordering in a prominent way. This paper presents various conditions, not involving well ordering, on a function $ h:N \times X \to \tau $ such that if a space $ (X,\tau )$ has a function satisfying one of these conditions, then it may be proved (using the axiom of choice) that it has a primitive base. These conditions are used in some characterizations of base of countable order. Examples show nonequivalence of the conditions with primitive base if the axiom of choice does not hold.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507338-6
Keywords: Primitive base, base of countable order, $ \theta $-space, first countable function, well ordering
Article copyright: © Copyright 1978 American Mathematical Society