Hereditary property of semi-separation axioms and its applications
Abstract
The paper studies the open-hereditary property of semi-separation axioms and
applies it to the study of digital topological spaces such as an $n$-dimensional Khalimsky topological space,
a Marcus-Wyse topological space and so on.
More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms
such as $T_{\frac{1}{2}}$, semi-$T_{\frac{1}{2}}$, semi-$T_1$, semi-$T_2$, {\it etc}.
Besides, using the finite or the infinite product property of the semi-$T_i$-separation axiom, $i\in \{1, 2\}$,
we confirm that the $n$-dimensional Khalimsky topological space is a semi-$T_2$-space.
After showing that not every subspace of the digital topological spaces satisfies the semi-$T_i$-separation axiom, $i\in \{1, 2\}$,
we prove that the semi-$T_i$-separation property is open-hereditary, $i\in \{1, 2\}$.
All spaces in the paper are assumed to be nonempty and connected.
applies it to the study of digital topological spaces such as an $n$-dimensional Khalimsky topological space,
a Marcus-Wyse topological space and so on.
More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms
such as $T_{\frac{1}{2}}$, semi-$T_{\frac{1}{2}}$, semi-$T_1$, semi-$T_2$, {\it etc}.
Besides, using the finite or the infinite product property of the semi-$T_i$-separation axiom, $i\in \{1, 2\}$,
we confirm that the $n$-dimensional Khalimsky topological space is a semi-$T_2$-space.
After showing that not every subspace of the digital topological spaces satisfies the semi-$T_i$-separation axiom, $i\in \{1, 2\}$,
we prove that the semi-$T_i$-separation property is open-hereditary, $i\in \{1, 2\}$.
All spaces in the paper are assumed to be nonempty and connected.
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