Cardinal invariants in remainders and variations of tightness

Authors:
A. V. ArhangelЬskii and A. Bella

Journal:
Proc. Amer. Math. Soc. **119** (1993), 947-954

MSC:
Primary 54A25; Secondary 54D35, 54D40, 54E35

MathSciNet review:
1185277

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper certain invariants related to the tightness are considered. Particular attention is given to the set tightness. Relations between properties of remainders and compactifications of a metrizable space are also investigated.

**[1]**A. V. Arhangel′skiĭ,*The structure and classification of topological spaces and cardinal invariants*, Uspekhi Mat. Nauk**33**(1978), no. 6(204), 29–84, 272 (Russian). MR**526012****[2]**A. V. Arhangel′skii, A. Bella, and F. Cammaroto,*Weak monolithicity, pseudoradial and weakly radial spaces*, Boll. Un. Mat. Ital. A (7)**5**(1991), no. 3, 339–344 (English, with Italian summary). MR**1138547****[3]**A. V. Arhangel′skiĭ, R. Isler, and G. Tironi,*On pseudoradial spaces*, Comment. Math. Univ. Carolin.**27**(1986), no. 1, 137–154. MR**843426****[4]**Angelo Bella,*Free sequences in pseudoradial spaces*, Comment. Math. Univ. Carolin.**27**(1986), no. 1, 163–170. MR**843428****[5]**A. Bella,*On set tightness and 𝑇-tightness*, Comment. Math. Univ. Carolin.**27**(1986), no. 4, 805–814. MR**874674****[6]**Ryszard Engelking,*General topology*, PWN—Polish Scientific Publishers, Warsaw, 1977. Translated from the Polish by the author; Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. MR**0500780****[7]**I. Juhász,*Variations on tightness*, Studia Sci. Math. Hungar.**24**(1989), no. 2-3, 179–186. MR**1051147****[8]**I. Juhàsz and Z. Szentmiklossy,*Converging free sequences in compact spaces*, preprint.**[9]**V. I. Malychin and B. E. Shapirovski,*Martin's axiom and properties of topological spaces*, Soviet Math. Dokl.**14**(1973), 1746-1751.**[10]**E. Michael,*A note on closed maps and compact sets*, Israel J. Math.**2**(1964), 173–176. MR**0177396****[11]**D. V. Ranchin,*Tightness, sequentiality and closed coverings*, Soviet Math. Dokl.**18**(1977), 196-200.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54A25,
54D35,
54D40,
54E35

Retrieve articles in all journals with MSC: 54A25, 54D35, 54D40, 54E35

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1185277-6

Keywords:
Tightness,
set tightness,
cardinal invariants,
remainder,
compactification,
topological groups,
monolithic spaces

Article copyright:
© Copyright 1993
American Mathematical Society