{
  "abstract": "Let $θ$ be an ordinal and let $(N_α)_{α\\leqθ}$ be a continuous increasing tower of closed normal subgroups of a Hausdorff topological group $G$, with $N_0=\\{e\\}$. Write $ρG$ for the Raikov completion of $G$, and put $K_α=\\overline{N_α}^{ρG}$ and $H_α=GK_α$. The successive and limit differences of the groups $H_α$ mark the first stages at which points of $ρG$ become old quotient points. For every nonzero ordinal $θ$ and every set $S\\subseteq(0,θ]$, there is a Hausdorff pseudocompact Boolean group with a continuous tower of closed normal subgroups such that every member of the tower is pseudocompact and the nonempty strata occur exactly at the stages in $S$. The terminal quotient can simultaneously be chosen isomorphic to $\\mathbb Z/2\\mathbb Z$, and for every $δ<θ$ the successive factor $N_{δ+1}/N_δ$ is compact exactly when $δ+1\\notin S$. Thus a tower may have a single nonempty stratum at a limit stage even when every successive factor is compact. For a closed normal subgroup $N$ of $G$, let $\\widehat q:ρG\\toρ(G/N)$ extend the quotient homomorphism and put $K=\\overline N^{ρG}$. Over $gN\\in G/N$, the fiber in $ρG\\setminus G$ is $g(K\\setminus N)$, homeomorphic to $ρN\\setminus N$, while for $y\\in\\widehat q(ρG)\\setminus(G/N)$ the entire $\\widehat q$-fiber lies in $ρG\\setminus G$ and is homeomorphic to $ρN$. For precompact kernels this gives a canonical decomposition, and nested quotients give the two-stage identity underlying the transfinite filtration. Further results concern pseudocompact Raikov remainders and include countable Abelian examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02212",
  "author_total": 1,
  "authors": [
    {
      "name": "Xing-Yu Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ep77ecb6hszjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02212",
  "fulltext_url": null,
  "id": "ep77ecb6hszjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02212",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.02212",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ep77ecb6hszjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.02212",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02212"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Arbitrary Stage Spectra for Raikov Remainders Along Quotient Towers",
  "title_text": "Arbitrary Stage Spectra for Raikov Remainders Along Quotient Towers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ep77ecb6hszjd",
  "venue": "arXiv",
  "versions": []
}