Namioka property of generalized ordered spaces
Abstract
A topological space $X$ is called Namioka, if for every compact space $K$ and every separately continuous function $f:X\times K\to\mathbb R$ there exists a dense $G_\delta$-set $A\subseteq X$ such that $f$ is jointly continuous at every point of $A\times K$. We introduce a notion of a topological space with countable resolvable set condition (i.e. in every separable subspace of such space each well-ordered strictly increasing (or decreasing) family of resolvable sets is at most countable) and prove that every hereditarily Baire perfect generalized ordered space with countable resolvable set condition is Namioka.
Fields of Study & Subjects
Advanced Topology and Set Theory
Fuzzy and Soft Set Theory
Advanced Algebra and Logic
Publication details
- Journal / source
- Carpathian Mathematical Publications
- Volume
- 18
- Issue
- 1
- Pages
- 5–10
- Publication date
- 3 January 2026