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Characterizations of z -Lindelöf spaces

Ahmad Al-Omari, Takashi Noiri (2017)

Archivum Mathematicum

A topological space ( X , τ ) is said to be z -Lindelöf  [1] if every cover of X by cozero sets of ( X , τ ) admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of z -Lindelöf spaces.

Compact images of spaces with a weaker metric topology

Peng-fei Yan, Cheng Lü (2008)

Czechoslovak Mathematical Journal

If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology. In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that (1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence { i } i of point-finite c s -covers such that i st ( y , i ) = { y } for each y Y . (2) Y is a sequentially-quotient...

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