6533b7d9fe1ef96bd126c248

RESEARCH PRODUCT

Introduction to generalized topological spaces

Irina Zvina

subject

Discrete mathematicsConnected spaceCompatible ideallcsh:Mathematicslcsh:QA299.6-433lcsh:AnalysisTopological spacelcsh:QA1-939Order generated by idealTopological vector spaceSeparation axiomSeparated setsModulo idealEmbeddingIdeal (order theory)FrameGeometry and TopologyGeneral topologyGeneralized topological spaceGeneralized topologyMathematicsgt-space

description

[EN] 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.

yearjournalcountryeditionlanguage
2011-04-01
10.4995/agt.2011.1701http://hdl.handle.net/10251/86979