• Honam Mathematical Journal
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• v.35 no.3
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• pp.541-550
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• 2013

In this paper, we strengthen the properties of approximation by points (AP) and weak approximation by points (WAP) considered by A. Pultr and A. Tozzi in 1993 to define ${\kappa}$-AP and ${\kappa}$-WAP for an infinite cardinal ${\kappa}$. We also strengthen the properties of radial and pseudoradial to define ${\kappa}$-radial and ${\kappa}$-pseudoradial for an infinite cardinal ${\kappa}$. These allow us to consider new cardinal functions related to almost closed sets; AP-number, WAP-number, radial number, and pseudoradial number. We study their properties and show the relationships between them. We also provide some examples around ${\kappa}$-AP and ${\kappa}$-WAP which are closely connected with ${\kappa}$-radial and ${\kappa}$-pseudoradial.

• Investigative Magnetic Resonance Imaging
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• v.18 no.3
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• pp.219-224
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• 2014

Purpose : To determine the incidence of truncated triangle appearance of anterior horn (AH) to body of medial meniscus (MM) and determine its clinical significance. Materials and Methods: IRB approval was obtained, and informed consent waived for this study. The criteria of "pseudoradial tear" was truncated triangle appearance of the tip of AH to body of MM on one or more coronal images with adjacent fluid signal intensity at the blunted tip. Two musculoskeletal radiologists retrospectively evaluated 485 knee MR images independently for the presence and number of sections with "pseudoradial tear" of AH to body of MM using proton density-weighted coronal MR images. Inter-and intraobserver agreement was calculated using kappa coefficients. Medical records were reviewed for arthroscopic correlation. Results: A pseudoradial tear in the AH to body of MM was present in 381 (78.6%) patients. Locations were 112 in AH (29.4%), 143 in AH to body (37.5%), and 126 in body (33.1%). Number of consecutive sections of pseudoradial tear were 1 in 100 (26.2%), 2 in 164 (43.0%), 3 in 94 (24.7%), 4 in 21 (5.5%), and 5 in 2 (0.5%). Interobserver agreement was 0.99 for presence and 0.43 for number of sections of pseudoradial tear. Arthroscopies were performed in 96 patients and none of the pseudoradial tears were proven as true radial tears on arthroscopy. Conclusion: Pseudoradial tears are frequently seen in AH to body of MM on coronal MR images and may be another pitfall that a radiologist needs to be aware of and be able to differentiate from true radial tear.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.447-452
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• 2008

We provide some examples around AP and WAP spaces which are connected with higher convergence properties-radiality, semiradiality and pseudoradiality. We also prove a theorem (Theorem 3.2) that (a) any pseudo-open continuous image of an AP-space is an AP-space and (b) any pseudo-open continuous image of an WAP-space is an WAP-space. This answers the question posed by V. V. Tkachuk and I. V. Yaschenko [10].

• Honam Mathematical Journal
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• v.39 no.4
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• pp.655-663
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• 2017

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.