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A topological space is locally connected at a point if every neighborhood of the point contains a connected open set containing the point.

A condition where a topological space can be divided into disjoint non-empty open sets.

A topological space where any two points can be connected by a continuous path.

A topological space that can be represented as the union of two or more disjoint non-empty open sets.

A maximal connected subspace of a given topological space.

A continuous transformation of one function or shape into another within a topological space, maintaining continuity throughout the transformation.

A topological space is locally path-connected at a point if every neighborhood of the point contains a path-connected open set containing the point.

A path-connected space where any loop can be continuously contracted to a point within the space.

A topological space that cannot be represented as the union of two or more disjoint non-empty open sets.

A maximal path-connected subspace of a given topological space.

A non-empty compact connected metric space.