Open AccessBounded sobriety and k-bounded sobriety of Q-cotopological spaces
Author(s) -
Yujing Zhang,
Kaiyun Wang
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1907095z
Subject(s) - bounded function , sobriety , mathematics , bounded operator , hausdorff space , bounded deformation , discrete mathematics , pure mathematics , mathematical analysis , psychology , psychotherapist
In this paper, we extend bounded sobriety and k-bounded sobriety to the setting of Q-cotopological spaces, whereQis a commutative and integral quantale. The main results are: (1) The category BSobQ-CTop of all bounded sober Q-cotopological spaces is a full reflective subcategory of the category SQ-CTop of all stratified Q-cotopological spaces; (2) We present the relationships among Hausdorff, T1, sobriety, bounded sobriety and k-bounded sobriety in the setting ofQ-cotopological spaces; (3) For a linearly ordered quantale Q, a topological space X is bounded (resp., k-bounded) sober if and only if the corresponding Q-cotopological space ?Q(X) is bounded (resp., k-bounded) sober, where ?Q : Top ? SQ-CTop is the well-known Lowen functor in fuzzy topology.