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Accessible and Biaccessible Points in Contrasequential Spaces a
Author(s) -
DOW ALAN,
VAUGHAN JERRY E.
Publication year - 1993
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1993.tb52512.x
Subject(s) - countable set , mathematics , cosmic space , closure (psychology) , point (geometry) , space (punctuation) , second countable space , sequence (biology) , set (abstract data type) , closed set , isolated point , combinatorics , discrete mathematics , compact space , pure mathematics , topological space , topological vector space , computer science , geometry , biology , economics , market economy , genetics , programming language , operating system
. Two countable spaces having no nontrivial convergent sequences are constructed. One space has every point biaccessible (by a countable discrete set), and the other has every point accessible but not biaccessible (by a countable discrete set). It is shown that in a compact T 2 ‐space if a set A is not closed, then there exists a free sequence contained in A whose closure is not contained in A . It follows that in a compact T 2 ‐space of countable tightness, every nonisolated point is biaccessible.