Paper Title:

Some Notes on the Semi-open Subspaces of Topological Spaces

Author(s):

Nicky. K. Tumalun, Philotheus E. A. Tuerah, and Rolles N. S. Palilingan

Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: nickytumalun@unima.ac.id
URL: https://fmipa.unima.ac.id/

Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: pheatuerah@unima.ac.id
URL: https://fmipa.unima.ac.id/

Department of Physics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: rollespalilingan@unima.ac.id
URL: https://fmipa.unima.ac.id/

Abstract:

In this paper, we obtain some new results regarding to the nowhere dense and first category set in the semi-open subspace of a topological space. More precisely, we prove that a nowhere dense set in the semi-open subspace of a topological space is equivalent as a nowhere dense set in that topological space. This implies that a first category set in the semi-open subspace of a topological space is equivalent as a first category set in that topological space. We also give some applications of these results to give some new proofs relating to the properties of semi-open set and Baire space.

Full Text PDF: