We consider operators simultaneously extending continuous pseudometrics defined on a certain class of closed subsets of the Euclidean space Rn" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">Rn��. Our result obtained for this class, with the assumption that the underlying space in general is not compact, is similar to that obtained by E. D. Tymchatyn and M. M. Zarichnyi for compact spaces.