User contributions for InfernalAtom683

15:3515:35, 1 April 2026 diff hist +241 Homeomorphism →Examples Tag: Visual edit

18:3618:36, 28 March 2026 diff hist +841 File:Hausdorff property in metric spaces.svg No edit summary current
18:2518:25, 28 March 2026 diff hist +345 N File:Hausdorff property in metric spaces.svg Uploaded own work with UploadWizard Tag: Upload Wizard
18:2518:25, 28 March 2026 diff hist +170 N Template:Created with TeX Created page with "50px|link=|alt=TeX logo This media was created with TeX. {{#if: {{{source|}}} | <syntaxhighlight lang="tex"> {{{source}}} </syntaxhighlight> }}" current
15:2915:29, 28 March 2026 diff hist +1,766 N Darboux integral Created page with "The '''Darboux integral''' is a formulation of integration in real analysis defined using upper and lower sums over partitions of an interval. It provides an order-theoretic approach to integration and is equivalent to the Riemann integral. == Definition == === Darboux sums === Let <math>f:[a,b]\to\mathbb{R}</math> be a bounded function. Let <math display="block"> P=\{x_0,x_1,\dots,x_n\}, \quad a=x_0 < x_1 < \cdots < x_n=b </math> be a partition of the interval..." Tag: Visual edit: Switched
14:2814:28, 28 March 2026 diff hist +566 N Template:Disambiguation Created page with "<templatestyles src="Disambiguation/styles.css"/> <div class="disambiguation metadata plainlinks"> <div class="disambiguation-image">30px|disambiguation</div> <div class="disambiguation-text">This is a disambiguation page, which lists pages which may be the intended target. If a [[Special:Whatlinkshere/{{PAGENAME}}|page link]] referred you here, please consider editing it to point directly to the intended..." current
14:2714:27, 28 March 2026 diff hist +488 N Template:Disambiguation/styles.css Created page with ".disambiguation { clear: both; margin: 0.9em 1em; border-top: 1px solid #ccc; border-bottom: 1px solid #ccc; display: flex; align-items: center; } .disambiguation-image { padding: 2px 0 2px 0.9em; text-align: center; →min-width, otherwise the image shrinks lots in minerva and timeless. * flex-basis can also be used: min-width: calc(0.9em + 30px); →left padding + image size: } .disambiguation-text { padding: 0.25em 0.9em; font-sty..." current

19:2919:29, 27 March 2026 diff hist +1,946 Homeomorphism No edit summary Tag: Visual edit: Switched

14:5114:51, 25 March 2026 diff hist +118 m Computation →Computability and its limits: Added TeX support for some functions current Tag: Visual edit: Switched
14:4614:46, 25 March 2026 diff hist +16 m Computation Used TeX formulas for numbers with exponents Tag: Visual edit
14:2514:25, 25 March 2026 diff hist +1,847 Topological space No edit summary Tag: Visual edit: Switched
13:3413:34, 25 March 2026 diff hist +225 Equivalence relation No edit summary

17:1417:14, 24 March 2026 diff hist +48 N MediaWiki:Tagline Created page with "From {{SITENAME}}, the mathematical encyclopedia" current
17:1417:14, 24 March 2026 diff hist +20 MediaWiki:Common.css No edit summary current
17:1317:13, 24 March 2026 diff hist +84 N MediaWiki:Common.css Created page with "→CSS placed here will be applied to all skins: #siteSub { display: block; }"
12:2912:29, 24 March 2026 diff hist −2 Locally Euclidean space No edit summary Tag: Visual edit
12:2912:29, 24 March 2026 diff hist +739 N Locally Euclidean space Created page with "A '''locally Euclidean space''' is a topological space that resembles a Euclidean space locally. Specifically, every point in a locally Euclidean space has an open neighborhood that is homeomorphic to an open subset in <math>\mathbb{R}^n</math>. The concept of locally Euclidean space is a central object in the definition of topological manifold. == Definition == A topological space <math>X</math> is locally Euclidean of dimension <math>n</math>, if for every..." Tag: Visual edit
09:5509:55, 24 March 2026 diff hist +29 N Hausdorffness InfernalAtom683 moved page Hausdorffness to Hausdorff space current Tag: New redirect
09:5509:55, 24 March 2026 diff hist 0 m Hausdorff space InfernalAtom683 moved page Hausdorffness to Hausdorff space
09:5409:54, 24 March 2026 diff hist +27 N Compactness InfernalAtom683 moved page Compactness to Compact space current Tag: New redirect
09:5409:54, 24 March 2026 diff hist 0 m Compact space InfernalAtom683 moved page Compactness to Compact space

22:5322:53, 22 March 2026 diff hist +1,214 N Topological space 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..." Tag: Visual edit
21:2121:21, 22 March 2026 diff hist +1,831 N Homotopy 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..." Tag: Visual edit
21:2021:20, 22 March 2026 diff hist +3,895 N Hausdorff space Created page with "A '''Hausdorff space''' (or '''<math>T_2</math> space''') is a type of topological space in which points can be "cleanly separated" by neighborhoods. Specifically, for any two distinct points, there exist disjoint open sets containing each point. Consequently, Hausdorff property ensures that limits of sequences are unique when they exist. == Definitions == A topological space <math>(X,\tau)</math> is Hausdorff, if for any two points <math>x,y\in X</math..." Tag: Visual edit
21:1921:19, 22 March 2026 diff hist +862 N Equivalence relation 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'..." Tag: Visual edit
20:5820:58, 22 March 2026 diff hist +1,038 N Compact space 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"...." Tag: Visual edit
20:5720:57, 22 March 2026 diff hist +899 N Category of topological spaces 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..." Tag: Visual edit
20:4220:42, 22 March 2026 diff hist +21,471 N Homeomorphism Created page with "thumb|250x250px|A homeomorphism that turns a coffee mug into a donut continuously. A '''homeomorphism''' is a special type of function between two topological spaces, that establishes that the two spaces are fundamentally the same from a topological perspective. Specifically, it is a continuous bijective function whose inverse function is also continuous. Homeomorphisms are the Isomorp..." Tag: Visual edit: Switched
20:1020:10, 22 March 2026 diff hist +427 N Template:Theorem Created page with "<templatestyles src="Theorem/styles.css" /><div class="theorem" style="{{{style|}}}"><strong>{{{title|Theorem}}}</strong> <div> {{#if: {{{theorem|<noinclude>y</noinclude>}}} | {{{theorem}}} | {{#if: {{{1| {{{continue|}}} }}} | {{{1| {{{continue}}} }}} | {{{1| {{error|Template:Theorem Error caused by a symbol in property: use <code>theorem</code> parameter}} }}} }} }} </div></div>" current
20:0920:09, 22 March 2026 diff hist +182 N Template:Theorem/styles.css Created page with ".theorem { 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; } }" current
20:0920:09, 22 March 2026 diff hist +434 N Template:Property 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>" current
20:0820:08, 22 March 2026 diff hist +183 N Template:Property/styles.css 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; } }" current
20:0820:08, 22 March 2026 diff hist +483 N Template:Proof 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..." current
20:0720:07, 22 March 2026 diff hist +319 N Template:Proof/styles.css 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; } }" current
20:0120:01, 22 March 2026 diff hist −1 Main Page No edit summary current
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20:0020:00, 22 March 2026 diff hist +4 Template:Main Page/Header No edit summary
19:5619:56, 22 March 2026 diff hist +1 Main Page No edit summary Tag: Visual edit
19:4919:49, 22 March 2026 diff hist 0 N File:Word mark.svg No edit summary current
19:4719:47, 22 March 2026 diff hist 0 N File:Mathepedia.png No edit summary current
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18:3718:37, 28 February 2026 diff hist +3,177 N Template:Main Page/Category ring No edit summary
00:0200:02, 28 February 2026 diff hist +2,427 N Template:Main Page/Button/styles.css Created page with ".main-cdx-button-link > a { background-color: var(--background-color-interactive-subtle, #f8f9fa); border: 1px solid var(--border-color-base, #a2a9b1); border-radius: 2px; padding: 0 0.85em; transition-property: background-color,color,border-color,box-shadow; transition-duration: .1s; box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 32px; min-height: 32px; max-width: 28em; font-family: inherit; font-s..."

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