Just as one is permitted to cook on Yom Tob, it is also permissible to carry on Yom Tob in a public domain, even in area that is not surrounded by an Erub. One may bring objects on Yom Tob from a private domain to a public domain, and vice versa, and carry objects within a public domain.
However, there are different views among the Halachic authorities as to how far this Halacha extends. The Shulhan Aruch held that one may carry in a public domain on Yom Tob even if this serves no purpose on Yom Tob. Although on Yom Tob one may not carry something for the specific purpose of preparing for the next day, it is permissible, according to the Shulhan Aruch, to carry something for no particular purpose on Yom Tob.
Others, however, ruled more stringently. The Rama (Rabbi Moshe Isserles of Cracow, 1525-1572) maintained that one may carry outdoors on Yom Tob only to serve some need on Yom Tob. For example, he may carry his Siddur home from the synagogue so he could use it later in the day. Similarly, one may carry home his Tallit if he fears that it might be taken if he leaves it in the synagogue. Furthermore, those who follow the practice not to wear a wristwatch on Shabbat in a place without an Erub may wear a watch outdoors on Yom Tob, since the watch serves the purpose of informing him of the time. By the same token, it would be permissible to carry a pocket watch in a public domain on Yom Tob. One may also carry a snuff box so he could use it for smelling.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) ruled even more stringently, allowing carrying in a public domain on Yom Tob only if this serves an immediate purpose. Thus, for example, it would be permissible in his view to carry one’s Siddur from the synagogue after Shaharit if he needs it when he arrives home, but not if he needs it only later, for Minha.
As for the final Halacha, Hacham Ovadia Yosef rules that one should follow the second position, that of the Rama, who allowed carrying on Yom Tob when this is necessary for any purpose. Even if that purpose is not immediate, it is nevertheless permissible to carry if the carrying serves some purpose on Yom Tob.
It should be noted that if one is taking a baby stroller outside on Yom Tob, and he fills the basket underneath the carriage with different items that are needed for the child, then the basket may also contain other items which are not needed. Since there is no extra action involved if the basket contains additional objects, it is permissible to bring the stroller outside even though it contains objects which one does not need.
It should also be clarified that the laws of Mukse apply equally on Shabbat and Yom Tob, and therefore one may not handle any Mukse objects on Yom Tob, even indoors, just like on Shabbat.
Summary: It is permissible to carry objects into and through a public domain on Yom Tob, even in an area without an Erub, provided that this serves some purpose on Yom Tob. For example, one may carry his Siddur home from synagogue so he could use it later that day. The laws of Mukse apply on Yom Tob just as on Shabbat.
