Countable open and closed functions

Abstract

We define two natural classes of functions, called 2-open and 2-closed, that are closest to open and closed functions. We show that they have the following property: there are $X_i\subset X$ $(i=1,2,...$) such that $f|X_i$ are open or closed functions onto $f(X_i)$ and $f(X_i)$ cover $Y.$

arXiv comment5 pages. arXiv admin note: substantial text overlap with arXiv:1102.3253