For mappings $f:S\to S$, where $S$ is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the $\delta$-entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the $\delta$-entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of $S^N$, which is closely connected with the $\delta$-entropy of $f:S\to S$.