Search results for "T1 space"

showing 2 items of 2 documents

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
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ON TOPOLOGICAL SPACES WITH A UNIQUE QUASI-PROXIMITY

1994

Abstract Trying to solve the question of whether every T 1 topological space with a unique compatible quasi-proximity should be hereditarily compact, we show that it is true for product spaces as well as for locally hereditarily Lindelof spaces.

Discrete mathematicsTopological manifoldPure mathematicsTopological tensor productHausdorff spaceMathematics::General TopologyTopological spaceSequential spaceTopological vector spaceMathematics::LogicMathematics (miscellaneous)T1 spaceLocally convex topological vector spaceMathematicsQuaestiones Mathematicae
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