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MHenry
MHenry
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Concerning a strongly nowhere dense open subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense open subset?

Concerning a strongly nowhere dense open subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense open subset?

Concerning a strongly nowhere dense subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense subset?

added 5 characters in body; edited title
Source Link
MHenry
MHenry
  • 139
  • 4

Concerning a strongly nowhere dense open subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense open subset?

Concerning a strongly nowhere dense subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense subset?

Concerning a strongly nowhere dense open subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense open subset?

Source Link
MHenry
MHenry
  • 139
  • 4

Concerning a strongly nowhere dense subset

A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

I need an example of a generalized topological space $X$ (which is not topological space) contains a strongly nowhere dense subset?