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In this article, the main properties of a somewhere dense set
[13] on topological spaces are studied and then it is used to generalize the
notions of interior, closure and boundary operators. The class of somewhere dense sets contains all α-open, pre-open, semi-open, β-open and bopen sets except for the empty set. We investigate under what conditions
the union of cs-dense sets and the intersection of somewhere dense sets
are cs-dense and somewhere dense, respectively. A concept of ST1-space
is defined and its various properties are discussed. Theorem (4.1) and
Corollary (4.14) give the answer for why we do not define ST0-spaces,
ST 1
2
-spaces, ST2-spaces and ST2
1
2
-spaces. Also, we point out that the
product of ST1-spaces is always an ST1-space and present some examples to illustrate the main results.
T. M. Al-shami. (2017) Somewhere Dense Sets and ST1-Spaces, Punjab University Journal of Mathematics, Volume 49, Issue 2.
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