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Questions tagged [generalized-topology]

A generalized topology, $\mu$ on a set $X$ is a collection of subsets of $X$ s.t. $\varphi\in\mu$ and arbitrary unions of members of $\mu$ belong to $\mu$; and the ordered pair $(X, \mu)$ then stands for a generalized topological space.

A generalized topology (GT, for short) $\mu$ on a set $X$ is a collection of subsets of $X$ such that $\varphi\in\mu$ and arbitrary unions of members of $\mu$ belong to $\mu$; and the ordered pair $(X,\mu)$ then stands for a generalized topological space (abbreviated as GTS).

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Monotonicity of semi closure of sets in generalized topological spaces

Hi I just want to ask if anybody here can show that if A is a subset of B then the semi closure of A is a subset of the semi closure of B. I know it is true for closure but I want to be sure if it holds for semi closure as well
user402701
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Union of semi open sets in generalized topological space

In order to define the semi closure of a set in a generalized topological space one must show first that the union of semi open sets is open. I found articles that cite Csaszar but they did not show how he proved it or what his remarks were. Does…
user402701
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Obtaining Generalized Topology by constructing Generalized neighbourhood

$X$ is a given set . To define Generalized Neighborhoods on $X$ Consider $ P ( P (X))$ - the power set of the power set of $X.$ Let $$\psi : X \rightarrow P(P(X))$$ satisfying $x\in V$ for $V\in \psi(x)$. Then $V\in \psi(x)$ is called a …
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