FoldUnfold Table of Contents The Hausdorff Property under Homeomorphisms on Topological Spaces The Hausdorff Property under Homeomorphisms on Topological Spaces Recall from the Hausdorff Topological Spaces page that a topological space $(X, \tau)$ is said to be Hausdorff if for every distinct pair of points $x, y \in X$ there exists open neighbourhoods $U$ of $x$ and $V$ … [Read more...]

## Second Countability under Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents Second Countability under Homeomorphisms on Topological Spaces Second Countability under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and open. Furthermore, if such a … [Read more...]

## First Countability under Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents First Countability under Homeomorphisms on Topological Spaces First Countability under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and open. Furthermore, if such a … [Read more...]

## The Boundary of a Set under Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents The Boundary of a Set under Homeomorphisms on Topological Spaces The Boundary of a Set under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and open. Furthermore, if … [Read more...]

## The Set of Accumulation Points under Homeomorphisms on Topological Spaces

FoldUnfold Table of Contents The Set of Accumulation Points under Homeomorphisms on Topological Spaces The Set of Accumulation Points under Homeomorphisms on Topological Spaces Recall from the Homeomorphisms on Topological Spaces page that if $X$ and $Y$ are topological spaces then a bijective map $f : X \to Y$ is said to be a homeomorphism if it is continuous and … [Read more...]