• Korean Journal of Mathematics
• /
• v.17 no.4
• /
• pp.411-417
• /
• 2009

The Urysohn's lemma which is crucial tool for the study of the metrization problem is proved in the sense of set-theoretic concept, namely, by the idempotent relation defined on a given topology.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.501-510
• /
• 2021

A uniform study towards normality is provided for topological spaces. Following Császár, 𝛄-normality and 𝛄(𝜃)-normality are introduced and investigated. For 𝛄 ∈ 𝚪₁₃, 𝛄-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as 𝜃-normality, 𝚫-normality etc. are shown to be particular cases of 𝛄(𝜃)-normality. In this process, 𝛄-regularity and 𝛄(𝜃)-regularity are introduced and studied. Several important characterizations of all these notions are provided.