


Paper's Title:
Some Notes on the Semiopen 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.
Email: nickytumalun@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email: pheatuerah@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Physics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email:
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 semiopen subspace of a topological space. More precisely, we prove that a nowhere dense set in the semiopen 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 semiopen 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 semiopen set and Baire space.
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