The Gelfand-Neimark theorem deals with proving two of these kinds of spaces to be homeomorphic to one another.
The Gelfand-Neimark theorem deals with proving two of these kinds of spaces to be homeomorphic to one another. Only Tychonoff spaces can be embedded in these types of spaces, and every topological space can be expressed as the quotient of spaces of this type. Etale spaces are the classical example of spaces failing to meet this condition, and if a space is both compact and meets this condition, it is normal and all continuous maps from compact spaces to these spaces are homeomorphisms. For 10 points, name this type of space defined as every point having disjoint neighborhoods around any pair of points, alternately called T2 and named after a German dude.
The Gelfand-Neimark theorem deals with proving two of these kinds of spaces to be homeomorphic to one another.
Hausdorff space [accept T2 before mentioned]