Jump to navigation Jump to search

General

Display information for equation id:math.231655.19 on revision:231655

* Page found: Homotopy lifting property (eq math.231655.19)

(force rerendering)

Occurrences on the following pages:

Hash: f6cb816a348385f439a173cc30f7048c

TeX (original user input):

T \colon = (X\times\{0\}) \cup (Y\times [0,1]) \ \subseteq \ X\times [0,1]

TeX (checked):

T\colon =(X\times \{0\})\cup (Y\times [0,1])\ \subseteq \ X\times [0,1]

LaTeXML (experimental; uses MathML) rendering

MathML (5.429 KB / 1.014 KB) :

T := ( X × { 0 } ) ( Y × [ 0 , 1 ] ) X × [ 0 , 1 ] assign 𝑇 𝑋 0 𝑌 0 1 𝑋 0 1 {\displaystyle T\colon=(X\times\{0\})\cup(Y\times[0,1])\ \subseteq\ X\times[0,% 1]}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle T\colon=(X\times\{0\})\cup(Y\times[0,1])\ \subseteq\ X\times[0,%&#10;1]}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">T</mi>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">:=</mo>
      <mrow id="p1.1.m1.1.31.2" xref="p1.1.m1.1.31.2.cmml">
        <mrow id="p1.1.m1.1.31.2.1" xref="p1.1.m1.1.31.2.1.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.31.2.1.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.31.2.1.2" xref="p1.1.m1.1.31.2.1.2.cmml">
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">X</mi>
            <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">×</mo>
            <mrow id="p1.1.m1.1.31.2.1.2.1" xref="p1.1.m1.1.31.2.1.2.1.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.7" xref="p1.1.m1.1.31.2.1.2.1.1.cmml">{</mo>
              <mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">0</mn>
              <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.31.2.1.2.1.1.cmml">}</mo>
            </mrow>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.31.2.1.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml"></mo>
        <mrow id="p1.1.m1.1.31.2.2" xref="p1.1.m1.1.31.2.2.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.31.2.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.31.2.2.2" xref="p1.1.m1.1.31.2.2.2.cmml">
            <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">Y</mi>
            <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">×</mo>
            <mrow id="p1.1.m1.1.31.2.2.2.1" xref="p1.1.m1.1.31.2.2.2.1.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.31.2.2.2.1.1.cmml">[</mo>
              <mn id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">0</mn>
              <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.31.2.2.2.1.1.cmml">,</mo>
              <mn id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">1</mn>
              <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.31.2.2.2.1.1.cmml">]</mo>
            </mrow>
          </mrow>
          <mo rspace="7.5pt" stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.31.2.2.2.cmml">)</mo>
        </mrow>
      </mrow>
      <mo rspace="7.5pt" id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml"></mo>
      <mrow id="p1.1.m1.1.31.3" xref="p1.1.m1.1.31.3.cmml">
        <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">X</mi>
        <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">×</mo>
        <mrow id="p1.1.m1.1.31.3.1" xref="p1.1.m1.1.31.3.1.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.26" xref="p1.1.m1.1.31.3.1.1.cmml">[</mo>
          <mn id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">0</mn>
          <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.31.3.1.1.cmml">,</mo>
          <mn id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">1</mn>
          <mo stretchy="false" id="p1.1.m1.1.30" xref="p1.1.m1.1.31.3.1.1.cmml">]</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">
        <and id="p1.1.m1.1.31a.cmml" xref="p1.1.m1.1.31"/>
        <apply id="p1.1.m1.1.31b.cmml" xref="p1.1.m1.1.31">
          <csymbol cd="latexml" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">assign</csymbol>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑇</ci>
          <apply id="p1.1.m1.1.31.2.cmml" xref="p1.1.m1.1.31.2">
            <union id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
            <apply id="p1.1.m1.1.31.2.1.2.cmml" xref="p1.1.m1.1.31.2.1">
              <times id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑋</ci>
              <set id="p1.1.m1.1.31.2.1.2.1.1.cmml" xref="p1.1.m1.1.31.2.1.2.1">
                <cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">0</cn>
              </set>
            </apply>
            <apply id="p1.1.m1.1.31.2.2.2.cmml" xref="p1.1.m1.1.31.2.2">
              <times id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
              <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑌</ci>
              <interval closure="closed" id="p1.1.m1.1.31.2.2.2.1.1.cmml" xref="p1.1.m1.1.31.2.2.2.1">
                <cn type="integer" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">0</cn>
                <cn type="integer" id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">1</cn>
              </interval>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.31c.cmml" xref="p1.1.m1.1.31">
          <subset id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22"/>
          <share href="#p1.1.m1.1.31.2.cmml" id="p1.1.m1.1.31d.cmml" xref="p1.1.m1.1.31"/>
          <apply id="p1.1.m1.1.31.3.cmml" xref="p1.1.m1.1.31.3">
            <times id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
            <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑋</ci>
            <interval closure="closed" id="p1.1.m1.1.31.3.1.1.cmml" xref="p1.1.m1.1.31.3.1">
              <cn type="integer" id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">0</cn>
              <cn type="integer" id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">1</cn>
            </interval>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle T\colon=(X\times\{0\})\cup(Y\times[0,1])\ \subseteq\ X\times[0,%
1]}</annotation>
  </semantics>
</math>

SVG (11.574 KB / 4.107 KB) :

upper T colon equals left-parenthesis upper X times StartSet 0 EndSet right-parenthesis union left-parenthesis upper Y times left-bracket 0 comma 1 right-bracket right-parenthesis subset-of-or-equal-to upper X times left-bracket 0 comma 1 right-bracket

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.327 KB / 439 B) :

T : = ( X × { 0 } ) ( Y × [ 0 , 1 ] )     X × [ 0 , 1 ] {\displaystyle T\colon =(X\times \{0\})\cup (Y\times [0,1])\ \subseteq \ X\times [0,1]}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle T\colon =(X\times \{0\})\cup (Y\times [0,1])\ \subseteq \ X\times [0,1]}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>T</mi>
        <mo>&#x003A;<!-- : --></mo>
        <mo>=</mo>
        <mo stretchy="false">(</mo>
        <mi>X</mi>
        <mo>&#x00D7;<!-- × --></mo>
        <mo fence="false" stretchy="false">{</mo>
        <mn>0</mn>
        <mo fence="false" stretchy="false">}</mo>
        <mo stretchy="false">)</mo>
        <mo>&#x222A;<!-- ∪ --></mo>
        <mo stretchy="false">(</mo>
        <mi>Y</mi>
        <mo>&#x00D7;<!-- × --></mo>
        <mo stretchy="false">[</mo>
        <mn>0</mn>
        <mo>,</mo>
        <mn>1</mn>
        <mo stretchy="false">]</mo>
        <mo stretchy="false">)</mo>
        <mtext>&#xA0;</mtext>
        <mo>&#x2286;<!-- ⊆ --></mo>
        <mtext>&#xA0;</mtext>
        <mi>X</mi>
        <mo>&#x00D7;<!-- × --></mo>
        <mo stretchy="false">[</mo>
        <mn>0</mn>
        <mo>,</mo>
        <mn>1</mn>
        <mo stretchy="false">]</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle T\colon =(X\times \{0\})\cup (Y\times [0,1])\ \subseteq \ X\times [0,1]}</annotation>
  </semantics>
</math>

SVG (9.081 KB / 3.789 KB) :

{\displaystyle T\colon =(X\times \{0\})\cup (Y\times [0,1])\ \subseteq \ X\times [0,1]}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Homotopy lifting property page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results