• In topology and related fields of mathematics, a sequential space is a topological space whose topology can be completely characterized by its convergent/divergent...
    29 KB (3,892 words) - 19:18, 2 June 2025
  • In mathematics, a topological space X is sequentially compact if every sequence of points in X has a convergent subsequence converging to a point in X...
    3 KB (432 words) - 00:15, 25 January 2025
  • identical to the sequential closure of S {\displaystyle S} in X . {\displaystyle X.} Fréchet–Urysohn spaces are a special type of sequential space. The property...
    20 KB (3,387 words) - 19:52, 9 April 2025
  • } (In other words, every first-countable space is a Fréchet-Urysohn space and thus also a sequential space.) This has consequences for limits and continuity...
    5 KB (837 words) - 11:38, 4 May 2025
  • the term T1 space is preferred. There is also a notion of a Fréchet–Urysohn space as a type of sequential space. The term symmetric space also has another...
    12 KB (1,928 words) - 18:28, 22 March 2025
  • after E. G. Pytkeev, who proved in 1983 that sequential spaces have this property. Let X be a topological space. For a subset S of X let S denote the closure...
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  • spaces are called US spaces. For sequential spaces, this notion is equivalent to being weakly Hausdorff. Subspaces and products of Hausdorff spaces are...
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  • Thumbnail for Metric space
    which is contained in the set. Every premetric space is a topological space, and in fact a sequential space. In general, the r {\displaystyle r} -balls themselves...
    82 KB (11,434 words) - 17:46, 21 May 2025
  • (this shortcoming of sequences motivated the study of sequential spaces and Fréchet–Urysohn spaces). Nets are in one-to-one correspondence with filters...
    46 KB (7,342 words) - 01:37, 4 June 2025
  • topology of a sequential space (or a Fréchet space) is determined by the convergent sequences. The countably generated spaces are precisely the spaces having...
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  • (reasonable) parallel machine is polynomially related to the space used by a sequential machine. The parallel computation thesis was set forth by Chandra...
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  • uniform space X is said to be sequentially complete or semi-complete if every Cauchy sequence in S converges to an element in S. X is called sequentially complete...
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  • Thumbnail for General topology
    σ-compact space: there exists a countable cover by compact spaces Relations: Every first countable space is sequential. Every second-countable space is first-countable...
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  • Thumbnail for Compact space
    a metric space, but may not be equivalent in other topological spaces. One such generalization is that a topological space is sequentially compact if...
    45 KB (5,704 words) - 03:15, 17 April 2025
  • which the sequential closure operator is defined, the topological space ( X , T ) {\displaystyle (X,{\mathcal {T}})} is a sequential space if and only...
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  • provably exist. Important countability axioms for topological spaces include: sequential space: a set is closed if and only if every convergent sequence in...
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  • compact space is limit point compact. For T1 spaces, countable compactness and limit point compactness are equivalent. Every sequentially compact space is...
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  • {\displaystyle X} is a sequential space (such as a pseudometrizable space) then this list may be extended to include: F {\displaystyle F} is sequentially continuous...
    30 KB (4,786 words) - 20:28, 9 June 2025
  • Particle filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems...
    95 KB (16,934 words) - 15:13, 4 June 2025
  • topological spaces whose definitions all somehow relate sequences in the codomain with sequences in the domain. Examples include sequentially quotient maps...
    26 KB (4,075 words) - 22:31, 2 January 2024
  • only if it is continuous. For LF spaces, a weaker converse holds; any bounded linear map from an LF space is sequentially continuous. If F : X → Y {\displaystyle...
    15 KB (2,456 words) - 19:12, 14 May 2025
  • locally convex topological vector space (such as any normed space) is continuous if and only if it is sequentially continuous at the origin. However,...
    128 KB (21,628 words) - 22:31, 27 May 2025
  • equivalent. Sequential spaces are CG-2. This includes first countable spaces, Alexandrov-discrete spaces, finite spaces. Every CG-3 space is a T1 space (because...
    30 KB (4,678 words) - 15:25, 21 April 2025
  • right-to-left script) or to the start of the next line. The effect of multiple sequential whitespace characters is cumulative such that the next printable character...
    26 KB (2,570 words) - 15:34, 18 May 2025
  • {\displaystyle X} is a metric space, sequential continuity and continuity are equivalent. For non-first-countable spaces, sequential continuity might be strictly...
    63 KB (9,309 words) - 11:22, 27 May 2025
  • \mathbb {R} ^{n}} is sequentially compact if and only if it is closed and bounded. The theorem is sometimes called the sequential compactness theorem....
    13 KB (2,066 words) - 16:49, 9 June 2025
  • Indexed Sequential Access Method (ISAM) is a method for creating, maintaining, and manipulating computer files of data so that records can be retrieved...
    10 KB (1,284 words) - 13:03, 31 May 2025
  • In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data...
    13 KB (1,504 words) - 11:24, 30 January 2025
  • Thumbnail for Hilbert space
    infinite-dimensional spaces, a set that is closed and bounded is not necessarily (sequentially) compact (as is the case in all finite dimensional spaces). Indeed...
    128 KB (17,469 words) - 06:51, 28 May 2025
  • Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space Second-countable space Separable...
    5 KB (401 words) - 16:43, 1 April 2025