On set star-Lindelöf spaces

[EN] A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆ SU, there is a countable subset V of U such that A ⊆ St(SV, U). The class of set star-Lindelöf spaces lie between the class of Lindel¨of spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set starLindelöf spaces.Singh, S. (2022). On set star-Lindelöf spaces. Applied General Topology. 23(2):315-323. https://doi.org/10.4995/agt.2022.1702131532323

Data-centric framework for digital twin development of an aircraft system

Poster presented at Cranfield University’s 2019 Manufacturing Doctoral Community event.Airbu

Remarks on monotonically star compact spaces

summary:A space $X$ is said to be monotonically star compact if one assigns to each open cover $\mathcal {U}$ a subspace $s(\mathcal {U}) \subseteq X$, called a kernel, such that $s(\mathcal {U})$ is a compact subset of $X$ and ${\rm St}(s(\mathcal {U}),\mathcal {U})=X$, and if $\mathcal {V}$ refines $\mathcal {U}$ then $s(\mathcal {U}) \subseteq s(\mathcal {V})$, where ${\rm St}(s(\mathcal {U}),\mathcal {U})= \bigcup \{U \in \nobreak \mathcal {U}\colon U \cap s(\mathcal {U}) \not = \emptyset \}$. We prove the following statements: \item {(1)} The inverse image of a monotonically star compact space under the open perfect map is monotonically star compact. \item {(2)} The product of a monotonically star compact space and a compact space is monotonically star compact. \item {(3)} If $X$ is monotonically star compact space with $e(X) < \omega$, then $A(X)$ is monotonically star compact, where $A(X)$ is the Alexandorff duplicate of space $X$. \endgraf The above statement (2) gives an answer to the question of Song (2015)