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"טומטום- מילה בשבת"
In the Gemara, ר' שיזבי says that a טומטום later discovered to be a זכר, is not given his ברית מילה on the 8th day if it falls out on שבת. Even though we learn that מילה בזמנה is דוחה שבת [שבת קלב.] from the pasuk "וביום השמיני", ר' שיזבי learns that the pasuk "אשה כי תזריע וילדה זכר", teaches us that in order for מילה to be דוחה שבת, the baby must be recognizable as a male from birth. Since this טומטום was indiscernible from birth, he is excluded from this לימוד.The רמ"א brings [יו"ד, רסו, י'] that it’s a מחלוקת: "טומטום שנקרע ונמצא זכר מלין אותו בשבת, ויש אוסרין".
The Gemara [עירובין מג.] discusses if traveling on Shabbos above 10 Tefachim from the ground (flying, boat) would be restricted by the תחום. The Gemara brings a story where someone gave a shiur on Shabbos in the Bais Medrash in פומפדיתא and סורא on the same Shabbos. Considering they are so far from each other, the Gemara assumes that it must have been אליהו הנביא who flew from one place to another, so we see that one may travel out of the תחום by flying. The Gemara suggests that this מגיד שיעור might have been a שד (demon) so the question remains unresolved. Consequently, we pasken לחומרא and one may not travel חוץ לתחום even if he is traveling 10 tefachim above the ground.
The [או"ח ס' רצה] רמ"א writes: "נהגו להזכיר אליהו הנביא במוצאי שבת להתפלל שיבוא ויבשרנו הגאולה". The ב"ח explains this מנהג and quotes the above, that traveling above 10 tefachim on Shabbos is a ספק איסור תחום, so אליהו can’t travel on Shabbos, so immediately after Shabbos is over when he may come, we mention his name and pray that he arrives speedily. The [ח"ו, ליקוטים ס' צח] חתם סופר asks, if אליהו is restricted by the תחום, why by a ברית מילה on Shabbos do we set a seat and say "זה הכסא של אליהו"? He can’t attend anyway! The Chasam Sofer answers that it was only the נשמה of אליהו that ascended to heaven and it is that neshama that attends a Bris. This neshama is not governed by the halacha of our world. When אליהו comes to announce Moshiach’s arrival, it will be in the גוף that was left behind. It is this bodily form that is restricted by the תחום. Hence, his announcement can’t be made on Shabbos (above ב"ח), but his neshama can attend a Bris. [ס' עח] שו"ת רמ"ע מפאנו brings the ספר אגודה that this is the reason we don’t say קידוש לבנה on ליל שבת ויו"ט, because (על פי קבלה) when we say קידוש לבנה and are מקבל פני השכינה that is in heaven, it is as if we are going חוץ לתחום. [ח"ד ס' קלג] שו"ת הרדב"ז brings this reason but doesn’t approve of it. He says the reason is that people should be home with their families on Friday night and it’s "לאו אורח ארעה" to be out.