A topological space is a fundamental concept in mathematics that generalizes the notion of geometric spaces, allowing for the definition of continuity, convergence, and boundary without requiring a specific notion of distance. It is defined by a set of points and a topology, which is a collection of open sets that satisfy certain axioms regarding unions, intersections, and the inclusion of the entire set and the empty set.

Topological Space

topological space

fundamental concept in mathematics

geometric spaces

definition of continuity

Definition of convergence

Definition of boundary

specific notion of distance

set of points

Topology is a branch of mathematics that studies the properties of space that are preserved under continuous transformations such as stretching and bending, but not tearing or gluing. It provides a foundational framework for understanding concepts of convergence, continuity, and compactness in various mathematical contexts.

topology

collection of open sets

certain axioms

Unions and intersections

inclusion of the entire set

The empty set, denoted by ∅ or {}, is a fundamental concept in set theory representing a set with no elements. It serves as the unique identity element for the operation of union in set theory and is a subset of every set.

empty set

Definition and Properties of Epsilon-Neighborhoods

Chain Complexes

Construction and Convergence of the Atiyah–Hirzebruch Spectral Sequence

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