On the pullback stability of a quotient map with respect to a closure operator

There are well-known characterizations of hereditary quotient maps in the category of topological spaces, (that is, of quotient maps stable under pullback along embeddings), as well as of universal quotient maps (that is, of quotient maps stable under pullback). These are precisely the so-called pse...

ver descrição completa

Detalhes bibliográficos
Autor principal: Sousa, Lurdes (author)
Formato: article
Idioma:eng
Publicado em: 2015
Assuntos:
Texto completo:http://hdl.handle.net/10400.19/2896
País:Portugal
Oai:oai:repositorio.ipv.pt:10400.19/2896
Descrição
Resumo:There are well-known characterizations of hereditary quotient maps in the category of topological spaces, (that is, of quotient maps stable under pullback along embeddings), as well as of universal quotient maps (that is, of quotient maps stable under pullback). These are precisely the so-called pseudo-open maps, as shown by Arhangel'slii, and the bi-quotient maps of Michael, as shown by Day and Kelly, respectively. In this paper hereditary and stable quotient maps are characterized in the broader context given by a category eqquipped with a closure operator. To this end, we derive explicit formulae and conditions for the closure in the codomain of such a quotient map in terms of the closure in its domain.