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22 March 2026
| N 22:53 | Topological space diffhist +1,214 InfernalAtom683 talk contribs (Created page with "A '''topological space''' is a fundamental mathematical structure that generalizes the concept of geometrical spaces and continuity. A topological space is equipped with a collection of open sets, capturing the intuitive idea of "nearness" without necessarily defining a metric. Topological spaces are the objects of study in general topology. == Definition == An ordered pair <math>(X, \tau)</math> is a topological space on set <math>X</math>, if <math...") | ||||
| N 21:21 | Homotopy diffhist +1,831 InfernalAtom683 talk contribs (Created page with "A '''homotopy''' is a continuous deformation between two continuous functions from one topological space to another. Specifically, a homotopy between two functions is a continuous map that, for each point in the domain, provides a path from its image under the first function to its image under the second. If such a function exists between two functions, they are said to be homotopic. Intuitively, a homotopy is the continuous transformation of...") | ||||
| N 21:19 | Equivalence relation diffhist +862 InfernalAtom683 talk contribs (Created page with "An '''equivalence relation''' is a binary relation on a set that groups elements into categories<ref>Not to be confused with category in category theory.</ref> in which all members are considered "equivalent" under some criterion. == Definition == A relation <math>\sim</math> on set <math>X</math> is a equivalence relation if it satisfies the following properties: * '''Reflexivity''': <math>\forall x\in X</math>, <math>x\sim x</math>. * '''Symmetry'...") | ||||
| N 20:58 | Compactness diffhist +1,038 InfernalAtom683 talk contribs (Created page with "A '''compact''' topological space is one that behaves, in many respects, like a finite space, even if it is infinite. Specifically, a compact space is a topological space whose every open cover admits a finite subcover. Compactness is one of the most fundamental topological properties in analysis and topology. Intuitively, compactness can be understood as a generalization of being "closed and bounded"....") | ||||
| N 20:57 | Category of topological spaces diffhist +899 InfernalAtom683 talk contribs (Created page with "The '''category of topological spaces''', denoted <math>\mathsf{Top}</math> or <math>\mathbf{Top}</math>, is the category whose objects are topological spaces and whose morphisms are continuous functions. == Definition == The category <math>\mathsf{Top}</math> consists of: * <math>\operatorname{ob}(\mathsf{Top})</math> consists of all topological spaces, * <math>\operatorname{mor}(\mathsf{Top})</math> consi...") | ||||
| N 20:09 | Template:Property diffhist +434 InfernalAtom683 talk contribs (Created page with "<templatestyles src="Property/styles.css" /><div class="property" style="{{{style|}}}"><strong>{{{title|Property}}}</strong> <div> {{#if: {{{property|<noinclude>y</noinclude>}}} | {{{property}}} | {{#if: {{{1| {{{continue|}}} }}} | {{{1| {{{continue}}} }}} | {{{1| {{error|Template:Property Error caused by a symbol in property: use <code>property</code> parameter}} }}} }} }} </div></div>") | ||||
| N 20:08 | Template:Property/styles.css diffhist +183 InfernalAtom683 talk contribs (Created page with ".property { border: thin solid #aaa; margin: 1em 2em; padding: 0.5em 1em 0.4em; } @media (max-width: 500px) { .property { margin: 1em 0; padding: 0.5em 0.5em 0.4em; } }") | ||||
| N 20:08 | Template:Proof diffhist +483 InfernalAtom683 talk contribs (Created page with "<templatestyles src="Proof/styles.css" /><div class="proof mw-collapsible" style="{{{style|}}}"><strong>{{{title|Proof}}}</strong> <div class="mw-collapsible-content"> {{#if: {{{proof|<noinclude>y</noinclude>}}} | {{{proof}}} | {{#if: {{{1| {{{continue|}}} }}} | {{{1| {{{continue}}} }}} | {{{1| {{error|Template:Proof Error caused by a symbol in proof: use <code>proof</code> parameter}} }}} }} }} <div class="qed">□</div> </di...") | ||||
| N 20:07 | Template:Proof/styles.css diffhist +319 InfernalAtom683 talk contribs (Created page with ".proof { border: thin solid #aaa; margin: 1em 2em; padding: 0.5em 1em 0.4em; } .proof::after { content: ""; display: table; clear: both; } .qed { float: right; clear: both; margin-top: 0.2em; font-size: 1.2em; } @media (max-width: 500px) { .proof { margin: 1em 0; padding: 0.5em 0.5em 0.4em; } }") | ||||