On the Metrizability of Spaces with a Sharp Base

A base for a space is said to be if, whenever ∈ and () is a sequence of pairwise distinct elements of each containing , the collection {∩ : ∈ } is a local base at . We answer questions raised by Alleche and Arhangel'skii by showing that a pseudocompact TychonofF space with a sharp base need not be metrizable and that the product of a space with a sharp base and [0,1] need not have a sharp base. We prove various metrization theorems and provide a characterization along the lines of Ponomarev's for point countable bases

Year of publication:	2018
Authors:	Good, Chris
Other Persons:	Knight, Robin (contributor) ; Mohamad, Abdul M. (contributor)
Publisher:	[2018]: [S.l.] : SSRN

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