On θ-extension of continuous mapping

2025/06/02 by Ryabikov, Andrew
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2506.02228

Abstract

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an extension are proved. The axioms of separation and compactness of spaces are not assumed.

Citations

• On extension functions for image space with different separation axioms

Related

• Continuous extension of functions from countable sets
• Various types of continuity and their interpretations in ideal topological spaces
• Extensions of Continuous Function in LG-Topology
• Extending continuous functions
• An Algebraic and Logical approach to continuous images