<story><title>Unicode Character “𝕏” (U+1D54F)</title><url>https://www.compart.com/en/unicode/U+1D54F</url></story><parent_chain><item><author>red_trumpet</author><text>Now that I think about it, most double stroked characters really represent &amp;quot;concrete&amp;quot; objects, not generic ones. Like ℙ for projective space, or 𝔸 for affine space. Also 𝔽 is often used together with an index 𝔽_q for &lt;i&gt;the&lt;/i&gt; field with q elements.&lt;p&gt;On the other hand, Wikipedia[1] agrees with you, that 𝕏 is &amp;quot;occasionally&amp;quot; used for metric spaces.&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Blackboard_bold&quot; rel=&quot;nofollow noreferrer&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Blackboard_bold&lt;/a&gt;</text></item><item><author>orlp</author><text>You&amp;#x27;re right I should&amp;#x27;ve used &amp;quot;as a symbol&amp;quot; not &amp;quot;as the symbol&amp;quot;. It&amp;#x27;s not terribly common.</text></item><item><author>red_trumpet</author><text>I&amp;#x27;m a PhD student in algebraic geometry and have seldom seen this. IME &amp;quot;X&amp;quot; is a generic name for all kinds of spaces (metric, topological, complex analytic, algebraic...), but I don&amp;#x27;t remember ever having seen &amp;quot;𝕏&amp;quot;.&lt;p&gt;That said, in principal everyone is free to call their spaces how they like. It just makes it easier to read if one sticks to familiar notation.</text></item><item><author>orlp</author><text>𝕏 is used as a symbol for a generic metric space. E.g. if your result is generic over ℝ², ℂ³, etc, you can write 𝕏.</text></item><item><author>dietrichepp</author><text>This is for math.&lt;p&gt;In Latex, you get these symbols with \mathbb{}. They are most commonly used to represent to represent number sets, like the set of all integers Z (from the German), set of all natural numbers N, set of complex numbers C, set of all real numbers R, rationals Q (for “quotient”), set of quaternions H (named after Hamilton), or an unknown set F (for “field”). This explains why many of the letters in this series exist in the basic multilingual plane—because R is very commonly used, but A is not. You can find ℝ in the basic multilingual plane at U+211D.&lt;p&gt;I don’t know why people are interested in the X symbol. It’s just there to complete the alphabet. There are many other ranges like this used for writing mathematical formulas, like the range of bold letters, fraktur, script, etc.</text></item></parent_chain><comment><author>ginnungagap</author><text>In set theory blackboard bold P, Q and C are very often used for arbitrary (forcing) posets</text></comment>
<story><title>Unicode Character “𝕏” (U+1D54F)</title><url>https://www.compart.com/en/unicode/U+1D54F</url></story><parent_chain><item><author>red_trumpet</author><text>Now that I think about it, most double stroked characters really represent &amp;quot;concrete&amp;quot; objects, not generic ones. Like ℙ for projective space, or 𝔸 for affine space. Also 𝔽 is often used together with an index 𝔽_q for &lt;i&gt;the&lt;/i&gt; field with q elements.&lt;p&gt;On the other hand, Wikipedia[1] agrees with you, that 𝕏 is &amp;quot;occasionally&amp;quot; used for metric spaces.&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Blackboard_bold&quot; rel=&quot;nofollow noreferrer&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Blackboard_bold&lt;/a&gt;</text></item><item><author>orlp</author><text>You&amp;#x27;re right I should&amp;#x27;ve used &amp;quot;as a symbol&amp;quot; not &amp;quot;as the symbol&amp;quot;. It&amp;#x27;s not terribly common.</text></item><item><author>red_trumpet</author><text>I&amp;#x27;m a PhD student in algebraic geometry and have seldom seen this. IME &amp;quot;X&amp;quot; is a generic name for all kinds of spaces (metric, topological, complex analytic, algebraic...), but I don&amp;#x27;t remember ever having seen &amp;quot;𝕏&amp;quot;.&lt;p&gt;That said, in principal everyone is free to call their spaces how they like. It just makes it easier to read if one sticks to familiar notation.</text></item><item><author>orlp</author><text>𝕏 is used as a symbol for a generic metric space. E.g. if your result is generic over ℝ², ℂ³, etc, you can write 𝕏.</text></item><item><author>dietrichepp</author><text>This is for math.&lt;p&gt;In Latex, you get these symbols with \mathbb{}. They are most commonly used to represent to represent number sets, like the set of all integers Z (from the German), set of all natural numbers N, set of complex numbers C, set of all real numbers R, rationals Q (for “quotient”), set of quaternions H (named after Hamilton), or an unknown set F (for “field”). This explains why many of the letters in this series exist in the basic multilingual plane—because R is very commonly used, but A is not. You can find ℝ in the basic multilingual plane at U+211D.&lt;p&gt;I don’t know why people are interested in the X symbol. It’s just there to complete the alphabet. There are many other ranges like this used for writing mathematical formulas, like the range of bold letters, fraktur, script, etc.</text></item></parent_chain><comment><author>dietrichepp</author><text>My experience with 𝔽 is “vector space over a field 𝔽”, which is not a concrete object, but I have probably seen F written in a normal italic style more often.</text></comment>