Introduction to generalized topological spaces

Irina Zvina


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.


Generalized topology; Generalized topological space; gt-space; Compatible ideal; Modulo ideal; Frame; Order generated by ideal

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