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$theta$-regularity in spaces with more topologies

Result description

The term {it space} $(X,tau,sigma,rho)$ is referred as a set $X$ with three, generally non-identical topologies $tau$, $sigma$ and $rho$. We say that $xin X$ is a {it $(sigma, rho)$-$theta$-cluster point} of a filter base $Phi$ in $X$ if forevery $Vinsigma$ such that $xin V$ and every $FinPhi$ the intersection $Fcapcl_rho V$ is non-empty. If $Phi$ has a cluster point with respect to the topology $tau$, we say that has a {it $tau$-cluster point}. medskip parindentt=0pt {bf Definition 1.} We say that a space $X$ is said to be {it(countably) $(tau,sigma,rho)$-$theta$-regular} if every (countable) $tau$-closed filter base $Phi$ with a $(sigma,rho)$-$theta$-cluster point has a $tau$-cluster point. medskip {bf Theorem A.} {sl Let $X$ be the product (sum) space for the family $left{X_iota |iotain Iright}$ of $(tau_iota,sigma_iota,rho_iota)$-$theta$-regular spaces $X_iota$ with the corresponding product (sum) t

Keywords

More topologies on a set$theta$-regularitypairwise paracompactness

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    $theta$-regularity in spaces with more topologies

  • Original language description

    The term {it space} $(X,tau,sigma,rho)$ is referred as a set $X$ with three, generally non-identical topologies $tau$, $sigma$ and $rho$. We say that $xin X$ is a {it $(sigma, rho)$-$theta$-cluster point} of a filter base $Phi$ in $X$ if forevery $Vinsigma$ such that $xin V$ and every $FinPhi$ the intersection $Fcapcl_rho V$ is non-empty. If $Phi$ has a cluster point with respect to the topology $tau$, we say that has a {it $tau$-cluster point}. medskip parindentt=0pt {bf Definition 1.} We say that a space $X$ is said to be {it(countably) $(tau,sigma,rho)$-$theta$-regular} if every (countable) $tau$-closed filter base $Phi$ with a $(sigma,rho)$-$theta$-cluster point has a $tau$-cluster point. medskip {bf Theorem A.} {sl Let $X$ be the product (sum) space for the family $left{X_iota |iotain Iright}$ of $(tau_iota,sigma_iota,rho_iota)$-$theta$-regular spaces $X_iota$ with the corresponding product (sum) t

  • Czech name

    $theta$-regularita v prostorech s více topologiemi

  • Czech description

    V práci zkoumáme modifikaci $theta$-regularity pro prostory s několika (dvěma a více) topologiemi. Důsledkem jsou některé zajímavé bitopologické pokrývací vlastnosti a modifikace parakompaktnosti.

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

Others

  • Publication year

    1999

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    III Congreso Iberoamericano De Topologia Y Sus Aplicaciones

  • ISBN

  • ISSN

  • e-ISSN

  • Number of pages

    1

  • Pages from-to

    65-65

  • Publisher name

    Escuela Universitaria de Gandia

  • Place of publication

  • Event location

    Gandia

  • Event date

    Apr 7, 1999

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

Basic information

Result type

D - Article in proceedings

D

CEP

BA - General mathematics

Year of implementation

1999