Spaces with σ-locally finite Lindelöf sn-networks | Zendy

Luong Quoc Tuyen | Zendy

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Spaces with σ-locally finite Lindelöf sn-networks

Author(s) -

Luong Quoc Tuyen

Publication year - 2013

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1307145t

Subject(s) - locally compact space , mathematics , separable space , quotient , metric space , space (punctuation) , second countable space , pure mathematics , characterization (materials science) , countable set , metric (unit) , discrete mathematics , quotient space (topology) , topology (electrical circuits) , mathematical analysis , combinatorics , computer science , physics , operations management , optics , economics , operating system

We prove that a space X has a σ-locally finite Lindelof sn-network if and only if X is a compact-covering compact and mssc-image of a locally separable metric space, if and only if X is a sequentially-quotient π and mssc-image of a locally separable metric space, where “compact-covering” (or “sequentially-quotient”) can not be replaced by “sequence-covering”. As an application, we give a new characterization of spaces with locally countable weak bases.

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