RECONSTRUCTION OF FINITE TOPOLOGICAL SPACES WITH MORE THAN ONE ISOLATED POINT

A. Anat Jaslin Jini and S. Monikandan

  DOI:
  https://doi.org/10.37418/amsj.9.4.2

Full Text

The deck of a topological space $X$ is the set $\mathscr{D}(X)=\{[X-\{x\}]:x\in X\},$ where $[Z]$ denotes the homeomorphism class of $Z.$ A space $X$ is topologically reconstructible if whenever $\mathscr{D}(X)=\mathscr{D}(Y)$ then $X$ is homeomorphic to $Y.$ For $|\mathscr{D}(X)|\geq 3,$ it is shown that all finite topological spaces with more than one isolated point are reconstructible.


Keywords:
Reconstruction, Finite topological space, Homeomorphism.