A functional characterization of primitive base

Wicke, Howard H.

doi:10.1090/S0002-9939-1978-0507338-6

A functional characterization of primitive base
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by Howard H. Wicke

Proc. Amer. Math. Soc. 72 (1978), 355-361

DOI: https://doi.org/10.1090/S0002-9939-1978-0507338-6

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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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The hereditary Lindelöf property, primitive structures, and separable metrizability

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