Search results for "Compatible ideal"

showing 2 items of 2 documents

Introduction to generalized topological spaces

2011

[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.

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
researchProduct

On i-topological spaces: generalization of the concept of a topological space via ideals

2006

[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.

Discrete mathematicsTopological manifoldPure mathematicsConnected spaceCompatible idealTopological algebralcsh:MathematicsGeneralizationlcsh:QA299.6-433lcsh:AnalysisTopological spacelcsh:QA1-939Topological vector spaceT1 spaceTrivial topologyGeometry and TopologyTopological spaceMathematicsZero-dimensional space
researchProduct