A stronger form of locally closed set and its homeomorphic image

Authors : Jiarul Hoque, Shyamapada Modak

Pages : 25-36

Doi:10.31801/cfsuasmas.1186168

View : 44 | Download : 140

Publication Date : 2024-03-16

Article Type : Research Paper

Abstract :Through this paper, via the operators $(\\cdot)^{\\star}$ and $\\Psi$, we presented notion of $\\star$-Locally set in an ideal topological space $\\zeta_{\\mathbb{I}}$ as a new stronger form of locally closed set, and considered relations with various existing weak form of locally closed set. Preservations of direct images as well as inverse images of $(\\cdot)^{\\star}$, $\\Psi$, $\\star$-perfect and various weak forms of locally closed set including $\\star$-Locally closed set are important investigating part. Besides, we pointed out that consideration of `bijectivity\' in Lemma 3.1 of [24] is sufficient, and the Lemma 3.3 of [24] is wrong. We demonstrated two modifications of the last one.
Keywords : Ideal, local function, \\Psi operator, locally closed set, homeomorphism