Compactly generated rectifiable spaces or paratopological groups

Lin, Fucai

Lin, Fucai

Mathematical Communications, Tome 18 (2013) no. 1, p. 417-427 / Harvested from Mathematical Communications

Text on Mathematical Communications

Résumé

A rectifiable space (or a paratopological group)

$G$ is compactly generated if

$G=~\langle K\rangle$ for some compact subset

$K$ of

$G$ . In this paper, we mainly discuss compactly generated rectifiable spaces or paratopological groups. The main results are that: (1) each

$\sigma$ -compact metrizable rectifiable space containing a dense compactly generated rectifiable subspace is compactly generated; (2) a metriable rectifiable space is compactly generated if and only if it is

$\sigma$ -compact and finitely generated modulo open sets; (3) any

$\sigma$ -compact paratopological group can be embedded as a closed paratopological subgroup in some compactly generated paratopological group. Finally, we consider generalized metric properties of compactly generated rectifiable spaces.

Publié le : 2013-11-12
Classification:

@article{mc482,
     author = {Lin, Fucai},
     title = {Compactly generated rectifiable spaces or paratopological groups},
     journal = {Mathematical Communications},
     volume = {18},
     number = {1},
     year = {2013},
     pages = { 417-427},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc482}
}

Lin, Fucai. Compactly generated rectifiable spaces or paratopological groups. Mathematical Communications, Tome 18 (2013) no. 1, pp.  417-427. http://gdmltest.u-ga.fr/item/mc482/