A separate continuous function not feebly continuous

2021/07/08 by Wojciech Bielas, Bielas, Wojciech
Mathematics · #54C08 #54C30 #54G20 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2107.03790

openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a separate continuous function f\colonℚ×ℚ→[0,1] and a dense subset D⊆ ℚ×ℚ such that f[D] is not dense in f[ℚ×ℚ], in other words, f is separate continuous and not feebly (somewhat) continuous.

Related

• No function is continuous only at points in a countable dense subset
• The set of bounded continuous nowhere locally uniformly continuous\n functions is not Borel
• A note on uniform continuity of monotone functions
• A generalization of a Baire theorem concerning barely continuous functions
• The discontinuity points set of separately continuous functions on the products of compacts