Hypersoft Semi-Connected Spaces

Florentin Smarandache; V.Inthumathi; M.Amsaveni

Authors

Florentin Smarandache Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA;
V.Inthumathi Department of Mathematics, Nallamuthu Gounder Mahalingam College, Tamil Nadu, India;
M.Amsaveni Department of Mathematics, Nallamuthu Gounder Mahalingam College, Tamil Nadu, India;

Keywords:

HSO sets, hypersoft semi-first countable spaces, hypersoft semi-separation, HSCO, HLSCO.

Abstract

Neutrosophic sets are an important field of topology that deals with inconsistent, indeterminate,
and uncertain circumstances in real life. Hypersoft sets have grown in popularity due to their ability to represent
data as a collection of trait-valued disjoint sets that combine various attributes. Motivated by this concept,
we introduce a new hyper-approach known as hypersoft semi-separated, which employs hypersoft semi-open
sets [HSO]. This article presents several local properties of HSO sets, such as hypersoft semi-neighborhoods of
hypersoft points and hypersoft semi-first countable spaces. Additionally, definitions of hypersoft semi-connected
[HSCO] spaces, hypersoft locally semi-connected [HLSCO] spaces, and associated properties are provided. The
comparison between hypersoft-connected [HCO] spaces, HSCO, and HLSCO spaces is presented along with
their examples.

DOI: 10.5281/zenodo.14688270