TY - JOUR
AU - Zvina, Irina
PY - 2011/04/01
Y2 - 2022/12/05
TI - Introduction to generalized topological spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 12
IS - 1
SE -
DO - 10.4995/agt.2011.1701
UR - https://polipapers.upv.es/index.php/AGT/article/view/1701
SP - 49-66
AB - We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
ER -