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• Bad math
  ...ut a more typical problem with how [[mathematics]] is used in applications is '''made-up and hidden parameters'''. Compare: ...sentation of the topology of gray scale images|graph representation of the topology of images]] (and [[Pixcavator]] in particular),
  3 KB (453 words) - 10:35, 26 February 2013
• How to compute Betti numbers
  The $k$-[[chain group]] $C_k(K)$ is given as a vector space with [[basis of vector space|basis]] consisting of Its dimension is then obvious.
  5 KB (890 words) - 14:47, 24 August 2014
• Simply connected spaces
  *Can you can get from $A$ to $B$ in two ([[topology|topologically]]) different ways? So, $X$ is called ''simply connected'' if every closed curve can be "contracted" -- vi
  5 KB (785 words) - 22:07, 3 January 2014
• Connectivity
  ...ent the object simply as a list of pairs of numbers and this is the way it is commonly done. ...ent" they are connected by an edge, as shown in these pictures. The result is a ''graph representation of the binary image''.
  4 KB (636 words) - 14:53, 9 October 2010
• Examples of homology of cubical complexes
  The simplest way to capture the [[topology]] of $X$ is by considering a square and an edge as on the right. Its cubical representa (This is called the $0$-[[skeleton]] of $K$.)
  3 KB (519 words) - 18:06, 27 August 2015
• Stages of analysis
  Suppose we have found the [[topology graph]] of the [[gray scale image]]. '''Image -> its topology graph -> one of the possible topologies'''
  1 KB (174 words) - 18:34, 30 January 2011
• Intro to Higher Mathematics -- Spring 2018 -- final exam
  *Show enough work to justify your answers. $\bullet$ '''2.''' Below is the addition (multiplication) table of a group. Complete it.
  2 KB (284 words) - 18:23, 4 May 2018
• Advanced Topology -- Spring 2013 -- final exam
  *Show enough work to justify your answers. Refer to theorems whenever necessary. #A set $Y \subset {\bf R}^n$ is called star-shaped if there is $a\in Y$ such that for any $x \in Y$ the segment from $x$ to $a$ lies entir
  3 KB (532 words) - 15:09, 8 May 2013
• Peter Saveliev
  Hello! My name is Peter Saveliev (rhymes with “leave”). Pronouns are available upon reque *''Topology Illustrated'' (Note: Due to my day job, the second edition is postponed indefinitely.)
  4 KB (652 words) - 14:02, 15 April 2024
• Topology I -- Fall 2013 -- final exam
  *Show enough work to justify your answers. Refer to theorems whenever necessary. ...Y U I O P [ ] \. Think of them as if they are made of wires so that there is no width in these lines. Classify them "up to homeomorphism". (Just the ans
  2 KB (317 words) - 16:34, 10 December 2013
• Topology I -- Fall 2013 -- midterm
  *Show enough work to justify your answers. Refer to theorems whenever necessary. #Show that any set is both open and closed relative to itself. (short proof)
  1 KB (241 words) - 17:53, 21 October 2013
• How to use Pixcavator
  Stage 1: automatic.</strong> The software creates a [[topology graph|data structure]] that contains the complete information about the con ...ntours so that the user can choose the best segmentation. The output table is also updated instantly.
  3 KB (442 words) - 14:43, 4 November 2011

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