*Definition [#idb63ec4]
For a topological space X, the character of x in X is defined by
#ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cchi%20%28x%2cX%29=%5cmin%20%5c%7b%20%7c%5cmathcal%7bU%7d%7c%20:%5cmathcal%7bU%7d%20%5ctext%7b%20is%20a%20neighborhood%20base%20of%20%7dx%5ctext%7b%20in%20%7dX%20%5c%7d%20+%5comega%20%5c%5d%7d%25.png);.

The character of X is defined by
#ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cchi%28X%29=%5csup%5c%7b%5cchi%28x%2cX%29:x%5cin%20X%5c%7d%20%5c%5d%7d%25.png);.

*Reference [#xf75f6a6]
K.P.Hart, J. Nagata and J.E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science