An Aspect of Eretz Yisroel in Every Country?

Question

According to Chazal, Eretz Yisroel is the birthplace of the world (ex: Rambam sefer Avodah Hilchos Bais Habechira 2:2). But, is there any source claiming that each nation and land has a "spark" or "piece" of Eretz Yisroel in it?

As the birthplace of the world, it stands to reason that it would pass on some (though, certainly not all) of its spiritual influence. EY is it's own spiritual and physical reality; so that's not the point of my question. What I'm asking is how this reality is influencing the rest of the world.

Answer 1

Taanit 10a:

ת"ר א"י נבראת תחילה וכל העולם כולו נברא לבסוף שנאמר (משלי ח, כו) עד לא עשה ארץ וחוצות א"י משקה אותה הקב"ה בעצמו וכל העולם כולו ע"י שליח שנאמר (איוב ה, י) הנותן מטר על פני ארץ ושולח מים על פני חוצות א"י שותה מי גשמים וכל העולם כולו מתמצית שנאמר הנותן מטר על פני ארץ וגו' א"י שותה תחילה וכל העולם כולו לבסוף שנאמר הנותן מטר על פני ארץ וגו'

Our Rabbis have taught: Israel was created first and then the rest of the world, as it is said, While as yet He had not made the earth, nor the fields. Israel is watered by the Holy One, blessed be He, and the rest of the world is watered by a messenger, as it is said, Who giveth rain upon the earth, and sendeth waters upon the fields. Israel is watered by the rain and the rest of the world is watered by the residue, as it is said, ‘ Who giveth rain upon the earth, etc’. Israel is watered first and then the rest of the world, as it is said, ‘Who giveth rain upon the earth, etc’.

Yalkut Shimoni, Yeshayahu 503:

עתידה ירושלים להיות כארץ ישראל וארץ ישראל, ככל העולם כלו

This is often quoted/interpreted as "Eretz Yisrael is destined to spread to all lands."

Berachot 8a:

אמרו ליה לר' יוחנן איכא סבי בבבל תמה ואמר (דברים יא, כא) למען ירבו ימיכם וימי בניכם על האדמה כתיב אבל בחוצה לארץ לא כיון דאמרי ליה מקדמי ומחשכי לבי כנישתא אמר היינו דאהני להו

When they told R. Yochanan that there were old men in Babylon, he showed astonishment and said: Why, it is written: That your days may be multiplied, and the days of your children, upon the land; but not outside the land [of Israel]! When they told him that they came early to the Synagogue and left it late, he said: That is what helps them.

The Vilna Gaon (Aderet Eliyahu, Devarim) explains based on Megillah 29a that the sanctity of synagogues stems from the sanctity of Eretz Yisrael, and therefore even though the verse specifies "upon the land," synagogues are included in this as well.

Answer 2

Here is what I ended up finding. It's a bit esoteric, but the basic idea is that the whole world is connected to and "spiritually nourished" by the area where the Kadosh Kadoshim once stood. The floor of the Kadosh Kadoshim consisted of a big stone called Even Shetiyah, the "Foundation Stone."

From the sefer Mishkeney Elyon by Rabbi Moshe Chaim Luzzatto:

"Know that there is one particular place known to her [The Shechina] in which all these roots are merged in unity. That place is the root of all things. There the Earth is rooted and all that is in it, the Heavens and the Heavens of the Heavens and all their hosts.

And at this meeting point where all the different roots come together in one place, in the middle can be seen a certain "stone". This stone is most precious. It includes every kind of charm and beauty. This is called Evven Shetiyah, the Foundation Stone. And thus there actually is such a stone in our world here down below in the place of the Holy of Holies in the Temple.

From this stone tracks and pathways extend in all directions leading to all the individual things that exist. Where these paths and tracks start leading off from the stone in all directions they are major general paths."

From Rebbe Nachman of Breslov:

"The world has a foundation stone. Channels emanate from this stone, reaching every land. The Midrash teaches us that the wise King Solomon knew the details of these channels and was therefore able to plant all types of trees. If people knew the exact location of these subterranean channels, they would be able to grow fruit trees even in these lands."