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Answer by F. A. Mala for Subsets with Trivial topology
In the trivial topology, where the only open sets are the entire space $X$ and the empty set $\emptyset$, let's address your questions:$\textbf{Compactness:}$Every subset of $X$ is compact in the...
View ArticleAnswer by Lee Mosher for Subsets with Trivial topology
"... compact also means bounded ..." is true in a metric space, where the concept of bounded is defined. But in a topological space where no metric is defined, boundedness is undefined. So you have to...
View ArticleSubsets with Trivial topology
I was thinking about the trivial topology, in which the only open sets are $X$ and $\emptyset$, where $X$ is the entire space we are working in.My doubt is: are all the subset of $X$ compact and...
View ArticleAnswer by F. A. Mala for Is every subset of $X$ compact and connected under...
In the trivial topology, where the only open sets are the entire space $X$ and the empty set $\emptyset$, let's address your questions:$\textbf{Compactness:}$Every subset of $X$ is compact in the...
View ArticleAnswer by Lee Mosher for Is every subset of $X$ compact and connected under...
"... compact also means bounded ..." is true in a metric space, where the concept of bounded is defined. But in a topological space where no metric is defined, boundedness is undefined. So you have to...
View ArticleIs every subset of $X$ compact and connected under the trivial topology on $X$?
I was thinking about the trivial topology, in which the only open sets are $X$ and $\emptyset$, where $X$ is the entire space we are working in.My doubt is: are all the subset of $X$ compact and...
View Article
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